LMFDB - Embedded newform 58.2.d.a.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,2,Mod(7,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	58.d (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.463132331723$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	58.25
Dual form			58.2.d.a.7.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.222521 - 0.974928i) q^{2} +(0.500000 - 0.240787i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.0440730 + 0.193096i) q^{5} +(-0.123490 - 0.541044i) q^{6} +(-0.0990311 + 0.0476909i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-1.67845 + 2.10471i) q^{9} +(0.178448 + 0.0859360i) q^{10} +(-0.832437 - 1.04384i) q^{11} -0.554958 q^{12} +(2.45593 + 3.07964i) q^{13} +(0.0244587 + 0.107160i) q^{14} +(0.0244587 + 0.107160i) q^{15} +(0.623490 + 0.781831i) q^{16} -2.91185 q^{17} +(1.67845 + 2.10471i) q^{18} +(-1.16756 - 0.562269i) q^{19} +(0.123490 - 0.154851i) q^{20} +(-0.0380322 + 0.0476909i) q^{21} +(-1.20291 + 0.579289i) q^{22} +(-1.73341 - 7.59455i) q^{23} +(-0.123490 + 0.541044i) q^{24} +(4.46950 + 2.15240i) q^{25} +(3.54892 - 1.70907i) q^{26} +(-0.702907 + 3.07964i) q^{27} +0.109916 q^{28} +(-1.39493 - 5.20136i) q^{29} +0.109916 q^{30} +(2.07942 - 9.11052i) q^{31} +(0.900969 - 0.433884i) q^{32} +(-0.667563 - 0.321481i) q^{33} +(-0.647948 + 2.83885i) q^{34} +(-0.00484434 - 0.0212244i) q^{35} +(2.42543 - 1.16802i) q^{36} +(-1.88740 + 2.36672i) q^{37} +(-0.807979 + 1.01317i) q^{38} +(1.96950 + 0.948461i) q^{39} +(-0.123490 - 0.154851i) q^{40} +3.76271 q^{41} +(0.0380322 + 0.0476909i) q^{42} +(1.48307 + 6.49777i) q^{43} +(0.297093 + 1.30165i) q^{44} +(-0.332437 - 0.416863i) q^{45} -7.78986 q^{46} +(0.500000 + 0.626980i) q^{47} +(0.500000 + 0.240787i) q^{48} +(-4.35690 + 5.46337i) q^{49} +(3.09299 - 3.87849i) q^{50} +(-1.45593 + 0.701137i) q^{51} +(-0.876510 - 3.84024i) q^{52} +(-1.85474 + 8.12615i) q^{53} +(2.84601 + 1.37057i) q^{54} +(0.238250 - 0.114735i) q^{55} +(0.0244587 - 0.107160i) q^{56} -0.719169 q^{57} +(-5.38135 + 0.202542i) q^{58} -5.08815 q^{59} +(0.0244587 - 0.107160i) q^{60} +(9.96346 - 4.79815i) q^{61} +(-8.41939 - 4.05456i) q^{62} +(0.0658433 - 0.288478i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.702907 + 0.338502i) q^{65} +(-0.461968 + 0.579289i) q^{66} +(-6.85839 + 8.60015i) q^{67} +(2.62349 + 1.26341i) q^{68} +(-2.69537 - 3.37989i) q^{69} -0.0217703 q^{70} +(6.82640 + 8.56003i) q^{71} +(-0.599031 - 2.62453i) q^{72} +(-1.76875 - 7.74940i) q^{73} +(1.88740 + 2.36672i) q^{74} +2.75302 q^{75} +(0.807979 + 1.01317i) q^{76} +(0.132219 + 0.0636733i) q^{77} +(1.36294 - 1.70907i) q^{78} +(3.04892 - 3.82322i) q^{79} +(-0.178448 + 0.0859360i) q^{80} +(-1.40701 - 6.16451i) q^{81} +(0.837282 - 3.66837i) q^{82} +(10.5184 + 5.06540i) q^{83} +(0.0549581 - 0.0264664i) q^{84} +(0.128334 - 0.562269i) q^{85} +6.66487 q^{86} +(-1.94989 - 2.26480i) q^{87} +1.33513 q^{88} +(2.55765 - 11.2058i) q^{89} +(-0.480386 + 0.231342i) q^{90} +(-0.390084 - 0.187854i) q^{91} +(-1.73341 + 7.59455i) q^{92} +(-1.15399 - 5.05596i) q^{93} +(0.722521 - 0.347948i) q^{94} +(0.160030 - 0.200671i) q^{95} +(0.346011 - 0.433884i) q^{96} +(9.54288 + 4.59561i) q^{97} +(4.35690 + 5.46337i) q^{98} +3.59419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} + q^{8} - 6 q^{9} - 3 q^{10} - 6 q^{11} - 4 q^{12} + 11 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - 10 q^{17} + 6 q^{18} - 6 q^{19} - 4 q^{20}+ \cdots + 48 q^{99}+O(q^{100}) $ 6 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 + q^8 - 6 * q^9 - 3 * q^10 - 6 * q^11 - 4 * q^12 + 11 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - 10 * q^17 + 6 * q^18 - 6 * q^19 - 4 * q^20 + 15 * q^21 + 6 * q^22 - 7 * q^23 + 4 * q^24 + 17 * q^25 + 3 * q^26 + 9 * q^27 + 2 * q^28 + 15 * q^29 + 2 * q^30 + 4 * q^31 + q^32 - 3 * q^33 + 10 * q^34 + 22 * q^35 + q^36 - 13 * q^37 - 15 * q^38 + 2 * q^39 + 4 * q^40 - 12 * q^41 - 15 * q^42 - 7 * q^43 + 15 * q^44 - 3 * q^45 + 3 * q^47 + 3 * q^48 - 18 * q^49 + 4 * q^50 - 5 * q^51 - 10 * q^52 - 22 * q^53 + 12 * q^54 - 24 * q^55 - 9 * q^56 + 18 * q^57 - 15 * q^58 - 38 * q^59 - 9 * q^60 + 31 * q^61 - 18 * q^62 - 2 * q^63 - q^64 + 9 * q^65 - 18 * q^66 + 11 * q^67 + 11 * q^68 - 28 * q^69 + 6 * q^70 + 23 * q^71 - 8 * q^72 + 5 * q^73 + 13 * q^74 + 26 * q^75 + 15 * q^76 + 12 * q^77 + 19 * q^78 + 3 * q^80 - 23 * q^81 - 16 * q^82 + 35 * q^83 + q^84 - 26 * q^85 + 42 * q^86 + 11 * q^87 + 6 * q^88 + 13 * q^89 + 10 * q^90 - q^91 - 7 * q^92 - 12 * q^93 + 4 * q^94 + 25 * q^95 - 3 * q^96 + 20 * q^97 + 18 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{4}{7}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$	0.500000	−	0.240787i	0.288675	−	0.139019i	−0.283942	−	0.958841i	$-0.591642\pi$
$3$	0.500000	−	0.240787i	0.288675	−	0.139019i	0.572617	+	0.819823i	$0.305928\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.0440730	+	0.193096i	−0.0197100	+	0.0863553i	−0.983826	−	0.179125i	$-0.942673\pi$
$5$	−0.0440730	+	0.193096i	−0.0197100	+	0.0863553i	0.964116	+	0.265480i	$0.0855305\pi$
$6$	−0.123490	−	0.541044i	−0.0504145	−	0.220880i
$7$	−0.0990311	+	0.0476909i	−0.0374302	+	0.0180255i	−0.452505	−	0.891762i	$-0.649470\pi$
$7$	−0.0990311	+	0.0476909i	−0.0374302	+	0.0180255i	0.415075	+	0.909787i	$0.363755\pi$
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$	−1.67845	+	2.10471i	−0.559483	+	0.701569i
$10$	0.178448	+	0.0859360i	0.0564302	+	0.0271753i
$11$	−0.832437	−	1.04384i	−0.250989	−	0.314731i	0.640336	−	0.768095i	$-0.278795\pi$
$11$	−0.832437	−	1.04384i	−0.250989	−	0.314731i	−0.891325	+	0.453364i	$0.850224\pi$
$12$	−0.554958			−0.160203
$13$	2.45593	+	3.07964i	0.681152	+	0.854137i	0.995460	−	0.0951839i	$-0.0303439\pi$
$13$	2.45593	+	3.07964i	0.681152	+	0.854137i	−0.314308	+	0.949321i	$0.601772\pi$
$14$	0.0244587	+	0.107160i	0.00653685	+	0.0286398i
$15$	0.0244587	+	0.107160i	0.00631520	+	0.0276687i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−2.91185			−0.706228			−0.353114	−	0.935580i	$-0.614877\pi$
$17$	−2.91185			−0.706228			−0.353114	+	0.935580i	$0.614877\pi$
$18$	1.67845	+	2.10471i	0.395614	+	0.496084i
$19$	−1.16756	−	0.562269i	−0.267857	−	0.128993i	0.295135	−	0.955456i	$-0.404635\pi$
$19$	−1.16756	−	0.562269i	−0.267857	−	0.128993i	−0.562992	+	0.826462i	$0.690350\pi$
$20$	0.123490	−	0.154851i	0.0276132	−	0.0346258i
$21$	−0.0380322	+	0.0476909i	−0.00829931	+	0.0104070i
$22$	−1.20291	+	0.579289i	−0.256461	+	0.123505i
$23$	−1.73341	−	7.59455i	−0.361440	−	1.58357i	−0.749542	−	0.661956i	$-0.769726\pi$
$23$	−1.73341	−	7.59455i	−0.361440	−	1.58357i	0.388102	−	0.921616i	$-0.373131\pi$
$24$	−0.123490	+	0.541044i	−0.0252073	+	0.110440i
$25$	4.46950	+	2.15240i	0.893900	+	0.430480i
$26$	3.54892	−	1.70907i	0.696000	−	0.335176i
$27$	−0.702907	+	3.07964i	−0.135274	+	0.592676i
$28$	0.109916			0.0207722
$29$	−1.39493	−	5.20136i	−0.259032	−	0.965869i
$29$	−1.39493	−	5.20136i	−0.259032	−	0.965869i
$30$	0.109916			0.0200679
$31$	2.07942	−	9.11052i	0.373474	−	1.63630i	−0.343467	−	0.939165i	$-0.611601\pi$
$31$	2.07942	−	9.11052i	0.373474	−	1.63630i	0.716942	−	0.697133i	$-0.245541\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$	−0.667563	−	0.321481i	−0.116208	−	0.0559627i
$34$	−0.647948	+	2.83885i	−0.111122	+	0.486858i
$35$	−0.00484434	−	0.0212244i	−0.000818843	−	0.00358758i
$36$	2.42543	−	1.16802i	0.404238	−	0.194671i
$37$	−1.88740	+	2.36672i	−0.310286	+	0.389086i	−0.912384	−	0.409336i	$-0.865760\pi$
$37$	−1.88740	+	2.36672i	−0.310286	+	0.389086i	0.602098	+	0.798422i	$0.294332\pi$
$38$	−0.807979	+	1.01317i	−0.131071	+	0.164358i
$39$	1.96950	+	0.948461i	0.315372	+	0.151875i
$40$	−0.123490	−	0.154851i	−0.0195255	−	0.0244841i
$41$	3.76271			0.587636			0.293818	−	0.955861i	$-0.405074\pi$
$41$	3.76271			0.587636			0.293818	+	0.955861i	$0.405074\pi$
$42$	0.0380322	+	0.0476909i	0.00586850	+	0.00735886i
$43$	1.48307	+	6.49777i	0.226167	+	0.990901i	0.952734	+	0.303806i	$0.0982574\pi$
$43$	1.48307	+	6.49777i	0.226167	+	0.990901i	−0.726567	+	0.687095i	$0.758885\pi$
$44$	0.297093	+	1.30165i	0.0447885	+	0.196231i
$45$	−0.332437	−	0.416863i	−0.0495568	−	0.0621423i
$46$	−7.78986			−1.14855
$47$	0.500000	+	0.626980i	0.0729325	+	0.0914545i	0.816959	−	0.576695i	$-0.195658\pi$
$47$	0.500000	+	0.626980i	0.0729325	+	0.0914545i	−0.744027	+	0.668150i	$0.767087\pi$
$48$	0.500000	+	0.240787i	0.0721688	+	0.0347547i
$49$	−4.35690	+	5.46337i	−0.622414	+	0.780482i
$50$	3.09299	−	3.87849i	0.437415	−	0.548501i
$51$	−1.45593	+	0.701137i	−0.203871	+	0.0981789i
$52$	−0.876510	−	3.84024i	−0.121550	−	0.532546i
$53$	−1.85474	+	8.12615i	−0.254768	+	1.11621i	0.671992	+	0.740558i	$0.265439\pi$
$53$	−1.85474	+	8.12615i	−0.254768	+	1.11621i	−0.926760	+	0.375654i	$0.877418\pi$
$54$	2.84601	+	1.37057i	0.387293	+	0.186510i
$55$	0.238250	−	0.114735i	0.0321257	−	0.0154709i
$56$	0.0244587	−	0.107160i	0.00326843	−	0.0143199i
$57$	−0.719169			−0.0952562
$58$	−5.38135	+	0.202542i	−0.706606	+	0.0265951i
$59$	−5.08815			−0.662420			−0.331210	−	0.943557i	$-0.607457\pi$
$59$	−5.08815			−0.662420			−0.331210	+	0.943557i	$0.607457\pi$
$60$	0.0244587	−	0.107160i	0.00315760	−	0.0138344i
$61$	9.96346	−	4.79815i	1.27569	−	0.614340i	0.331411	−	0.943486i	$-0.392475\pi$
$61$	9.96346	−	4.79815i	1.27569	−	0.614340i	0.944279	+	0.329146i	$0.106761\pi$
$62$	−8.41939	−	4.05456i	−1.06926	−	0.514930i
$63$	0.0658433	−	0.288478i	0.00829547	−	0.0363448i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−0.702907	+	0.338502i	−0.0871848	+	0.0419860i
$66$	−0.461968	+	0.579289i	−0.0568643	+	0.0713056i
$67$	−6.85839	+	8.60015i	−0.837885	+	1.05068i	0.160092	+	0.987102i	$0.448821\pi$
$67$	−6.85839	+	8.60015i	−0.837885	+	1.05068i	−0.997977	+	0.0635730i	$0.979750\pi$
$68$	2.62349	+	1.26341i	0.318145	+	0.153210i
$69$	−2.69537	−	3.37989i	−0.324485	−	0.406891i
$70$	−0.0217703			−0.00260204
$71$	6.82640	+	8.56003i	0.810144	+	1.01589i	0.999423	+	0.0339653i	$0.0108136\pi$
$71$	6.82640	+	8.56003i	0.810144	+	1.01589i	−0.189279	+	0.981923i	$0.560615\pi$
$72$	−0.599031	−	2.62453i	−0.0705965	−	0.309303i
$73$	−1.76875	−	7.74940i	−0.207017	−	0.906999i	−0.966539	−	0.256518i	$-0.917425\pi$
$73$	−1.76875	−	7.74940i	−0.207017	−	0.906999i	0.759523	−	0.650481i	$-0.225432\pi$
$74$	1.88740	+	2.36672i	0.219405	+	0.275125i
$75$	2.75302			0.317891
$76$	0.807979	+	1.01317i	0.0926815	+	0.116219i
$77$	0.132219	+	0.0636733i	0.0150678	+	0.00725625i
$78$	1.36294	−	1.70907i	0.154322	−	0.193514i
$79$	3.04892	−	3.82322i	0.343030	−	0.430146i	−0.580153	−	0.814508i	$-0.697007\pi$
$79$	3.04892	−	3.82322i	0.343030	−	0.430146i	0.923183	+	0.384362i	$0.125578\pi$
$80$	−0.178448	+	0.0859360i	−0.0199511	+	0.00960794i
$81$	−1.40701	−	6.16451i	−0.156334	−	0.684946i
$82$	0.837282	−	3.66837i	0.0924623	−	0.405104i
$83$	10.5184	+	5.06540i	1.15455	+	0.556000i	0.910396	−	0.413737i	$-0.135777\pi$
$83$	10.5184	+	5.06540i	1.15455	+	0.556000i	0.244150	+	0.969737i	$0.421491\pi$
$84$	0.0549581	−	0.0264664i	0.00599642	−	0.00288773i
$85$	0.128334	−	0.562269i	0.0139198	−	0.0609866i
$86$	6.66487			0.718692
$87$	−1.94989	−	2.26480i	−0.209050	−	0.242812i
$88$	1.33513			0.142325
$89$	2.55765	−	11.2058i	0.271110	−	1.18781i	−0.637595	−	0.770372i	$-0.720071\pi$
$89$	2.55765	−	11.2058i	0.271110	−	1.18781i	0.908705	−	0.417439i	$-0.137072\pi$
$90$	−0.480386	+	0.231342i	−0.0506371	+	0.0243855i
$91$	−0.390084	−	0.187854i	−0.0408919	−	0.0196925i
$92$	−1.73341	+	7.59455i	−0.180720	+	0.791786i
$93$	−1.15399	−	5.05596i	−0.119663	−	0.524278i
$94$	0.722521	−	0.347948i	0.0745223	−	0.0358881i
$95$	0.160030	−	0.200671i	0.0164187	−	0.0205884i
$96$	0.346011	−	0.433884i	0.0353146	−	0.0442831i
$97$	9.54288	+	4.59561i	0.968932	+	0.466613i	0.850285	−	0.526323i	$-0.176430\pi$
$97$	9.54288	+	4.59561i	0.968932	+	0.466613i	0.118648	+	0.992936i	$0.462144\pi$
$98$	4.35690	+	5.46337i	0.440113	+	0.551884i
$99$	3.59419			0.361229
$100$	−3.09299	−	3.87849i	−0.309299	−	0.387849i
$101$	−1.32908	−	5.82310i	−0.132249	−	0.579420i	−0.997012	−	0.0772410i	$-0.975389\pi$
$101$	−1.32908	−	5.82310i	−0.132249	−	0.579420i	0.864764	−	0.502179i	$-0.167468\pi$
$102$	0.359584	+	1.57544i	0.0356041	+	0.155992i
$103$	−8.97434	−	11.2535i	−0.884268	−	1.10884i	−0.993388	−	0.114809i	$-0.963374\pi$
$103$	−8.97434	−	11.2535i	−0.884268	−	1.10884i	0.109119	−	0.994029i	$-0.465197\pi$
$104$	−3.93900			−0.386251
$105$	−0.00753275	−	0.00944576i	−0.000735121	−	0.000921812i
$106$	7.50969	+	3.61648i	0.729405	+	0.351263i
$107$	−10.2823	+	12.8936i	−0.994030	+	1.24647i	−0.0249596	+	0.999688i	$0.507946\pi$
$107$	−10.2823	+	12.8936i	−0.994030	+	1.24647i	−0.969070	+	0.246785i	$0.920626\pi$
$108$	1.96950	−	2.46968i	0.189515	−	0.237645i
$109$	−2.55980	+	1.23274i	−0.245185	+	0.118075i	−0.552441	−	0.833552i	$-0.686303\pi$
$109$	−2.55980	+	1.23274i	−0.245185	+	0.118075i	0.307256	+	0.951627i	$0.400589\pi$
$110$	−0.0588430	−	0.257808i	−0.00561046	−	0.0245810i
$111$	−0.373822	+	1.63782i	−0.0354816	+	0.155455i
$112$	−0.0990311	−	0.0476909i	−0.00935756	−	0.00450636i
$113$	−14.1223	+	6.80094i	−1.32851	+	0.639778i	−0.957388	−	0.288804i	$-0.906742\pi$
$113$	−14.1223	+	6.80094i	−1.32851	+	0.639778i	−0.371125	+	0.928583i	$0.621028\pi$
$114$	−0.160030	+	0.701137i	−0.0149882	+	0.0656675i
$115$	1.54288			0.143874
$116$	−1.00000	+	5.29150i	−0.0928477	+	0.491304i
$117$	−10.6039			−0.980329
$118$	−1.13222	+	4.96058i	−0.104229	+	0.456658i
$119$	0.288364	−	0.138869i	0.0264343	−	0.0127301i
$120$	−0.0990311	−	0.0476909i	−0.00904026	−	0.00435356i
$121$	2.05107	−	8.98634i	0.186461	−	0.816940i
$122$	−2.46077	−	10.7813i	−0.222788	−	0.976097i
$123$	1.88135	−	0.906013i	0.169636	−	0.0816924i
$124$	−5.82640	+	7.30607i	−0.523226	+	0.656104i
$125$	−1.23005	+	1.54244i	−0.110019	+	0.137960i
$126$	−0.266594	−	0.128385i	−0.0237501	−	0.0114374i
$127$	−1.68867	−	2.11752i	−0.149845	−	0.187900i	0.701244	−	0.712922i	$-0.252629\pi$
$127$	−1.68867	−	2.11752i	−0.149845	−	0.187900i	−0.851089	+	0.525022i	$0.824057\pi$
$128$	−1.00000			−0.0883883
$129$	2.30612	+	2.89178i	0.203042	+	0.254607i
$130$	0.173604	+	0.760607i	0.0152260	+	0.0667097i
$131$	3.25182	+	14.2472i	0.284113	+	1.24478i	0.892466	+	0.451115i	$0.148973\pi$
$131$	3.25182	+	14.2472i	0.284113	+	1.24478i	−0.608353	+	0.793667i	$0.708169\pi$
$132$	0.461968	+	0.579289i	0.0402091	+	0.0504207i
$133$	0.142440			0.0123511
$134$	6.85839	+	8.60015i	0.592474	+	0.742939i
$135$	−0.563687	−	0.271458i	−0.0485145	−	0.0233633i
$136$	1.81551	−	2.27658i	0.155679	−	0.195215i
$137$	−0.993959	+	1.24639i	−0.0849197	+	0.106486i	−0.822476	−	0.568799i	$-0.807408\pi$
$137$	−0.993959	+	1.24639i	−0.0849197	+	0.106486i	0.737557	+	0.675285i	$0.235979\pi$
$138$	−3.89493	+	1.87570i	−0.331558	+	0.159670i
$139$	−0.287168	−	1.25816i	−0.0243573	−	0.106716i	0.961288	−	0.275545i	$-0.0888585\pi$
$139$	−0.287168	−	1.25816i	−0.0243573	−	0.106716i	−0.985645	+	0.168829i	$0.946001\pi$
$140$	−0.00484434	+	0.0212244i	−0.000409421	+	0.00179379i
$141$	0.400969	+	0.193096i	0.0337677	+	0.0162617i
$142$	9.86443	−	4.75046i	0.827804	−	0.398650i
$143$	1.17025	−	5.12721i	0.0978613	−	0.428758i
$144$	−2.69202			−0.224335
$145$	1.06584	−	0.0401160i	0.0885135	−	0.00333145i
$146$	−7.94869			−0.657838
$147$	−0.862937	+	3.78077i	−0.0711738	+	0.311833i
$148$	2.72737	−	1.31343i	0.224188	−	0.107963i
$149$	6.03415	+	2.90589i	0.494337	+	0.238060i	0.664406	−	0.747372i	$-0.268685\pi$
$149$	6.03415	+	2.90589i	0.494337	+	0.238060i	−0.170069	+	0.985432i	$0.554399\pi$
$150$	0.612605	−	2.68400i	0.0500190	−	0.219147i
$151$	2.11260	+	9.25593i	0.171921	+	0.753237i	0.985207	+	0.171371i	$0.0548198\pi$
$151$	2.11260	+	9.25593i	0.171921	+	0.753237i	−0.813285	+	0.581865i	$0.802323\pi$
$152$	1.16756	−	0.562269i	0.0947018	−	0.0456060i
$153$	4.88740	−	6.12860i	0.395122	−	0.495468i
$154$	0.0914984	−	0.114735i	0.00737315	−	0.00924564i
$155$	1.66756	+	0.803056i	0.133942	+	0.0645030i
$156$	−1.36294	−	1.70907i	−0.109122	−	0.136835i
$157$	9.39373			0.749701			0.374851	−	0.927085i	$-0.377694\pi$
$157$	9.39373			0.749701			0.374851	+	0.927085i	$0.377694\pi$
$158$	−3.04892	−	3.82322i	−0.242559	−	0.304159i
$159$	1.02930	+	4.50967i	0.0816290	+	0.357640i
$160$	0.0440730	+	0.193096i	0.00348428	+	0.0152656i
$161$	0.533852	+	0.669429i	0.0420734	+	0.0527584i
$162$	−6.32304			−0.496785
$163$	−10.1434	−	12.7194i	−0.794492	−	0.996262i	−0.999846	−	0.0175740i	$-0.994406\pi$
$163$	−10.1434	−	12.7194i	−0.794492	−	0.996262i	0.205353	−	0.978688i	$-0.434166\pi$
$164$	−3.39008	−	1.63258i	−0.264721	−	0.127483i
$165$	0.0914984	−	0.114735i	0.00712314	−	0.00893213i
$166$	7.27897	−	9.12754i	0.564958	−	0.708435i
$167$	12.3998	−	5.97142i	0.959523	−	0.462082i	0.112508	−	0.993651i	$-0.464112\pi$
$167$	12.3998	−	5.97142i	0.959523	−	0.462082i	0.847015	+	0.531569i	$0.178397\pi$
$168$	−0.0135735	−	0.0594696i	−0.00104722	−	0.00458818i
$169$	−0.559802	+	2.45265i	−0.0430617	+	0.188666i
$170$	−0.519614	−	0.250233i	−0.0398526	−	0.0191920i
$171$	3.14310	−	1.51364i	0.240359	−	0.115751i
$172$	1.48307	−	6.49777i	0.113083	−	0.495450i
$173$	−0.119605			−0.00909340			−0.00454670	−	0.999990i	$-0.501447\pi$
$173$	−0.119605			−0.00909340			−0.00454670	+	0.999990i	$0.501447\pi$
$174$	−2.64191	+	1.39703i	−0.200283	+	0.105909i
$175$	−0.545269			−0.0412185
$176$	0.297093	−	1.30165i	0.0223943	−	0.0981157i
$177$	−2.54407	+	1.22516i	−0.191224	+	0.0920887i
$178$	−10.3557	−	4.98704i	−0.776192	−	0.373795i
$179$	2.82155	−	12.3620i	0.210893	−	0.923981i	−0.753069	−	0.657941i	$-0.771428\pi$
$179$	2.82155	−	12.3620i	0.210893	−	0.923981i	0.963962	−	0.266040i	$-0.0857153\pi$
$180$	0.118645	+	0.519820i	0.00884331	+	0.0387451i
$181$	−6.42812	+	3.09562i	−0.477798	+	0.230095i	−0.657252	−	0.753671i	$-0.728281\pi$
$181$	−6.42812	+	3.09562i	−0.477798	+	0.230095i	0.179454	+	0.983766i	$0.442567\pi$
$182$	−0.269946	+	0.338502i	−0.0200098	+	0.0250914i
$183$	3.82640	−	4.79815i	0.282855	−	0.354689i
$184$	7.01842	+	3.37989i	0.517405	+	0.249169i
$185$	−0.373822	−	0.468758i	−0.0274839	−	0.0344638i
$186$	−5.18598			−0.380255
$187$	2.42394	+	3.03952i	0.177256	+	0.222272i
$188$	−0.178448	−	0.781831i	−0.0130147	−	0.0570209i
$189$	−0.0772609	−	0.338502i	−0.00561990	−	0.0246224i
$190$	−0.160030	−	0.200671i	−0.0116098	−	0.0145582i
$191$	3.19806			0.231404			0.115702	−	0.993284i	$-0.463088\pi$
$191$	3.19806			0.231404			0.115702	+	0.993284i	$0.463088\pi$
$192$	−0.346011	−	0.433884i	−0.0249712	−	0.0313129i
$193$	13.5782	+	6.53893i	0.977382	+	0.470682i	0.853204	−	0.521578i	$-0.174656\pi$
$193$	13.5782	+	6.53893i	0.977382	+	0.470682i	0.124178	+	0.992260i	$0.460371\pi$
$194$	6.60388	−	8.28100i	0.474131	−	0.594541i
$195$	−0.269946	+	0.338502i	−0.0193313	+	0.0242406i
$196$	6.29590	−	3.03194i	0.449707	−	0.216567i
$197$	3.23072	+	14.1547i	0.230179	+	1.00848i	0.949491	+	0.313794i	$0.101600\pi$
$197$	3.23072	+	14.1547i	0.230179	+	1.00848i	−0.719312	+	0.694687i	$0.755543\pi$
$198$	0.799782	−	3.50407i	0.0568380	−	0.249024i
$199$	−23.9013	−	11.5102i	−1.69432	−	0.815939i	−0.994860	−	0.101264i	$-0.967711\pi$
$199$	−23.9013	−	11.5102i	−1.69432	−	0.815939i	−0.699456	−	0.714676i	$-0.746574\pi$
$200$	−4.46950	+	2.15240i	−0.316041	+	0.152198i
$201$	−1.35839	+	5.95149i	−0.0958133	+	0.419785i
$202$	−5.97285			−0.420248
$203$	0.386199	+	0.448572i	0.0271058	+	0.0314835i
$204$	1.61596			0.113140
$205$	−0.165834	+	0.726566i	−0.0115823	+	0.0507455i
$206$	−12.9683	+	6.24521i	−0.903545	+	0.435124i
$207$	18.8937	+	9.09874i	1.31321	+	0.632406i
$208$	−0.876510	+	3.84024i	−0.0607750	+	0.266273i
$209$	0.385002	+	1.68681i	0.0266312	+	0.116679i
$210$	−0.0108851	+	0.00524200i	−0.000751145	+	0.000361733i
$211$	−10.4743	+	13.1344i	−0.721084	+	0.904210i	−0.998399	−	0.0565688i	$-0.981984\pi$
$211$	−10.4743	+	13.1344i	−0.721084	+	0.904210i	0.277315	+	0.960779i	$0.410555\pi$
$212$	5.19687	−	6.51666i	0.356922	−	0.447566i
$213$	5.47434	+	2.63631i	0.375096	+	0.180637i
$214$	10.2823	+	12.8936i	0.702885	+	0.881390i
$215$	−1.32006			−0.0900274
$216$	−1.96950	−	2.46968i	−0.134008	−	0.168040i
$217$	0.228562	+	1.00139i	0.0155158	+	0.0679791i
$218$	0.632219	+	2.76993i	0.0428193	+	0.187603i
$219$	−2.75033	−	3.44881i	−0.185850	−	0.233049i
$220$	−0.264438			−0.0178284
$221$	−7.15130	−	8.96745i	−0.481049	−	0.603216i
$222$	1.51357	+	0.728899i	0.101584	+	0.0489205i
$223$	−0.893436	+	1.12033i	−0.0598289	+	0.0750231i	−0.810846	−	0.585260i	$-0.800992\pi$
$223$	−0.893436	+	1.12033i	−0.0598289	+	0.0750231i	0.751017	+	0.660283i	$0.229564\pi$
$224$	−0.0685317	+	0.0859360i	−0.00457896	+	0.00574184i
$225$	−12.0320	+	5.79430i	−0.802133	+	0.386287i
$226$	3.48792	+	15.2816i	0.232013	+	1.01651i
$227$	2.98523	−	13.0791i	0.198137	−	0.868093i	−0.773908	−	0.633298i	$-0.781701\pi$
$227$	2.98523	−	13.0791i	0.198137	−	0.868093i	0.972045	−	0.234796i	$-0.0754421\pi$
$228$	0.647948	+	0.312036i	0.0429114	+	0.0206651i
$229$	−10.3693	+	4.99358i	−0.685221	+	0.329985i	−0.743899	−	0.668292i	$-0.767026\pi$
$229$	−10.3693	+	4.99358i	−0.685221	+	0.329985i	0.0586782	+	0.998277i	$0.481311\pi$
$230$	0.343322	−	1.50419i	0.0226380	−	0.0991836i
$231$	0.0814412			0.00535844
$232$	4.93631	+	2.15240i	0.324085	+	0.141312i
$233$	−0.735562			−0.0481883			−0.0240941	−	0.999710i	$-0.507670\pi$
$233$	−0.735562			−0.0481883			−0.0240941	+	0.999710i	$0.507670\pi$
$234$	−2.35958	+	10.3380i	−0.154251	+	0.675817i
$235$	−0.143104	+	0.0689153i	−0.00933508	+	0.00449554i
$236$	4.58426	+	2.20766i	0.298410	+	0.143707i
$237$	0.603875	−	2.64575i	0.0392259	−	0.171860i
$238$	−0.0712201	−	0.312036i	−0.00461651	−	0.0202263i
$239$	−0.0794168	+	0.0382451i	−0.00513705	+	0.00247387i	−0.436450	−	0.899728i	$-0.643765\pi$
$239$	−0.0794168	+	0.0382451i	−0.00513705	+	0.00247387i	0.431313	+	0.902202i	$0.358050\pi$
$240$	−0.0685317	+	0.0859360i	−0.00442370	+	0.00554714i
$241$	−3.87382	+	4.85762i	−0.249535	+	0.312907i	−0.890785	−	0.454425i	$-0.849845\pi$
$241$	−3.87382	+	4.85762i	−0.249535	+	0.312907i	0.641250	+	0.767332i	$0.278416\pi$
$242$	−8.30463	−	3.99930i	−0.533842	−	0.257085i
$243$	−8.09634	−	10.1525i	−0.519381	−	0.651283i
$244$	−11.0586			−0.707955
$245$	−0.862937	−	1.08209i	−0.0551310	−	0.0691321i
$246$	−0.464656	−	2.03579i	−0.0296254	−	0.129797i
$247$	−1.13587	−	4.97656i	−0.0722735	−	0.316651i
$248$	5.82640	+	7.30607i	0.369977	+	0.463936i
$249$	6.47889			0.410583
$250$	1.23005	+	1.54244i	0.0777954	+	0.0975524i
$251$	−13.6869	−	6.59128i	−0.863912	−	0.416038i	−0.0511894	−	0.998689i	$-0.516301\pi$
$251$	−13.6869	−	6.59128i	−0.863912	−	0.416038i	−0.812723	+	0.582651i	$0.802016\pi$
$252$	−0.184489	+	0.231342i	−0.0116217	+	0.0145731i
$253$	−6.48457	+	8.13139i	−0.407681	+	0.511216i
$254$	−2.44020	+	1.17514i	−0.153112	+	0.0737347i
$255$	−0.0712201	−	0.312036i	−0.00445997	−	0.0195404i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−4.98307	−	2.39972i	−0.310836	−	0.149691i	0.271962	−	0.962308i	$-0.412328\pi$
$257$	−4.98307	−	2.39972i	−0.310836	−	0.149691i	−0.582797	+	0.812618i	$0.698042\pi$
$258$	3.33244	−	1.60482i	0.207468	−	0.0999116i
$259$	0.0740400	−	0.324390i	0.00460062	−	0.0201566i
$260$	0.780167			0.0483839
$261$	13.2887	+	5.79430i	0.822547	+	0.358658i
$262$	14.6136			0.902829
$263$	−0.486959	+	2.13351i	−0.0300272	+	0.131558i	−0.987720	−	0.156235i	$-0.950064\pi$
$263$	−0.486959	+	2.13351i	−0.0300272	+	0.131558i	0.957693	+	0.287793i	$0.0929214\pi$
$264$	0.667563	−	0.321481i	0.0410857	−	0.0197858i
$265$	−1.48739	−	0.716287i	−0.0913694	−	0.0440012i
$266$	0.0316959	−	0.138869i	0.00194340	−	0.00851460i
$267$	−1.41939	−	6.21874i	−0.0868651	−	0.380581i
$268$	9.91066	−	4.77272i	0.605390	−	0.291540i
$269$	18.9901	−	23.8128i	1.15785	−	1.45189i	0.288642	−	0.957437i	$-0.406796\pi$
$269$	18.9901	−	23.8128i	1.15785	−	1.45189i	0.869203	−	0.494455i	$-0.164632\pi$
$270$	−0.390084	+	0.489150i	−0.0237397	+	0.0297687i
$271$	−28.4218	−	13.6872i	−1.72650	−	0.831440i	−0.987477	−	0.157765i	$-0.949571\pi$
$271$	−28.4218	−	13.6872i	−1.72650	−	0.831440i	−0.739027	−	0.673676i	$-0.764714\pi$
$272$	−1.81551	−	2.27658i	−0.110082	−	0.138038i
$273$	−0.240275			−0.0145421
$274$	0.993959	+	1.24639i	0.0600473	+	0.0752969i
$275$	−1.47381	−	6.45719i	−0.0888742	−	0.389383i
$276$	0.961968	+	4.21466i	0.0579037	+	0.253692i
$277$	8.85504	+	11.1039i	0.532048	+	0.667166i	0.973118	−	0.230306i	$-0.0739727\pi$
$277$	8.85504	+	11.1039i	0.532048	+	0.667166i	−0.441071	+	0.897472i	$0.645401\pi$
$278$	−1.29052			−0.0774003
$279$	15.6848	+	19.6681i	0.939023	+	1.17750i
$280$	0.0196143	+	0.00944576i	0.00117218	+	0.000564492i
$281$	12.9453	−	16.2329i	0.772254	−	0.968376i	−0.227732	−	0.973724i	$-0.573131\pi$
$281$	12.9453	−	16.2329i	0.772254	−	0.968376i	0.999986	+	0.00534795i	$0.00170231\pi$
$282$	0.277479	−	0.347948i	0.0165236	−	0.0207200i
$283$	15.6293	−	7.52667i	0.929065	−	0.447414i	0.0927662	−	0.995688i	$-0.470429\pi$
$283$	15.6293	−	7.52667i	0.929065	−	0.447414i	0.836299	+	0.548274i	$0.184715\pi$
$284$	−2.43631	−	10.6742i	−0.144569	−	0.633396i
$285$	0.0316959	−	0.138869i	0.00187750	−	0.00822588i
$286$	−4.73825	−	2.28182i	−0.280179	−	0.134927i
$287$	−0.372625	+	0.179447i	−0.0219954	+	0.0105924i
$288$	−0.599031	+	2.62453i	−0.0352982	+	0.154652i
$289$	−8.52111			−0.501242
$290$	0.198062	−	1.04805i	0.0116306	−	0.0615434i
$291$	5.87800			0.344575
$292$	−1.76875	+	7.74940i	−0.103508	+	0.453499i
$293$	−15.7920	+	7.60503i	−0.922579	+	0.444291i	−0.833991	−	0.551778i	$-0.813950\pi$
$293$	−15.7920	+	7.60503i	−0.922579	+	0.444291i	−0.0885879	+	0.996068i	$0.528235\pi$
$294$	3.49396	+	1.68260i	0.203772	+	0.0981313i
$295$	0.224250	−	0.982503i	0.0130563	−	0.0572035i
$296$	−0.673604	−	2.95125i	−0.0391524	−	0.171538i
$297$	3.79978	−	1.82988i	0.220486	−	0.106180i
$298$	4.17576	−	5.23624i	0.241895	−	0.303327i
$299$	19.1313	−	23.9899i	1.10639	−	1.38737i
$300$	−2.48039	−	1.19449i	−0.143205	−	0.0689640i
$301$	−0.456755	−	0.572753i	−0.0263269	−	0.0330129i
$302$	9.49396			0.546316
$303$	−2.06667	−	2.59152i	−0.118727	−	0.148879i
$304$	−0.288364	−	1.26341i	−0.0165388	−	0.0724613i
$305$	0.487386	+	2.13538i	0.0279076	+	0.122271i
$306$	−4.88740	−	6.12860i	−0.279394	−	0.350349i
$307$	30.3618			1.73284			0.866420	−	0.499316i	$-0.166415\pi$
$307$	30.3618			1.73284			0.866420	+	0.499316i	$0.166415\pi$
$308$	−0.0914984	−	0.114735i	−0.00521360	−	0.00653765i
$309$	−7.19687	−	3.46583i	−0.409415	−	0.197164i
$310$	1.15399	−	1.44706i	0.0655422	−	0.0821873i
$311$	−14.8312	+	18.5978i	−0.841003	+	1.05458i	0.156754	+	0.987638i	$0.449897\pi$
$311$	−14.8312	+	18.5978i	−0.841003	+	1.05458i	−0.997757	+	0.0669461i	$0.978674\pi$
$312$	−1.96950	+	0.948461i	−0.111501	+	0.0536961i
$313$	6.38069	+	27.9556i	0.360658	+	1.58015i	0.751529	+	0.659700i	$0.229317\pi$
$313$	6.38069	+	27.9556i	0.360658	+	1.58015i	−0.390871	+	0.920446i	$0.627826\pi$
$314$	2.09030	−	9.15821i	0.117963	−	0.516828i
$315$	0.0528022	+	0.0254282i	0.00297507	+	0.00143272i
$316$	−4.40581	+	2.12173i	−0.247846	+	0.119357i
$317$	1.68180	−	7.36845i	0.0944593	−	0.413853i	−0.905485	−	0.424378i	$-0.860493\pi$
$317$	1.68180	−	7.36845i	0.0944593	−	0.413853i	0.999945	+	0.0105243i	$0.00335006\pi$
$318$	4.62565			0.259393
$319$	−4.26822	+	5.78589i	−0.238974	+	0.323948i
$320$	0.198062			0.0110720
$321$	−2.03654	+	8.92267i	−0.113669	+	0.498015i
$322$	0.771438	−	0.371505i	0.0429906	−	0.0207032i
$323$	3.39977	+	1.63724i	0.189168	+	0.0910987i
$324$	−1.40701	+	6.16451i	−0.0781672	+	0.342473i
$325$	4.34817	+	19.0506i	0.241193	+	1.05674i
$326$	−14.6576	+	7.05875i	−0.811811	+	0.390948i
$327$	−0.983074	+	1.23274i	−0.0543641	+	0.0681705i
$328$	−2.34601	+	2.94180i	−0.129537	+	0.162434i
$329$	−0.0794168	−	0.0382451i	−0.00437839	−	0.00210852i
$330$	−0.0914984	−	0.114735i	−0.00503682	−	0.00631597i
$331$	−11.1860			−0.614837			−0.307419	−	0.951574i	$-0.599465\pi$
$331$	−11.1860			−0.614837			−0.307419	+	0.951574i	$0.599465\pi$
$332$	−7.27897	−	9.12754i	−0.399485	−	0.500939i
$333$	−1.81336	−	7.94483i	−0.0993713	−	0.435374i
$334$	−3.06249	−	13.4176i	−0.167572	−	0.734181i
$335$	−1.35839	−	1.70336i	−0.0742167	−	0.0930647i
$336$	−0.0609989			−0.00332776
$337$	−12.9641	−	16.2565i	−0.706201	−	0.885548i	0.291269	−	0.956641i	$-0.405923\pi$
$337$	−12.9641	−	16.2565i	−0.706201	−	0.885548i	−0.997470	+	0.0710934i	$0.977351\pi$
$338$	2.26659	+	1.09153i	0.123286	+	0.0593716i
$339$	−5.42357	+	6.80094i	−0.294568	+	0.369376i
$340$	−0.359584	+	0.450904i	−0.0195012	+	0.0244537i
$341$	−11.2409	+	5.41335i	−0.608731	+	0.293149i
$342$	−0.776283	−	3.40112i	−0.0419766	−	0.183911i
$343$	0.342126	−	1.49895i	0.0184731	−	0.0809358i
$344$	−6.00484	−	2.89178i	−0.323760	−	0.155914i
$345$	0.771438	−	0.371505i	0.0415328	−	0.0200012i
$346$	−0.0266146	+	0.116606i	−0.00143081	+	0.00626879i
$347$	0.0193774			0.00104023			0.000520116	−	1.00000i	$-0.499834\pi$
$347$	0.0193774			0.00104023			0.000520116		1.00000i	$0.499834\pi$
$348$	0.774127	+	2.88654i	0.0414975	+	0.154735i
$349$	29.0315			1.55402			0.777009	−	0.629489i	$-0.216736\pi$
$349$	29.0315			1.55402			0.777009	+	0.629489i	$0.216736\pi$
$350$	−0.121334	+	0.531598i	−0.00648557	+	0.0284151i
$351$	−11.2104	+	5.39866i	−0.598369	+	0.288159i
$352$	−1.20291	−	0.579289i	−0.0641151	−	0.0308762i
$353$	−4.58761	+	20.0996i	−0.244174	+	1.06980i	0.693001	+	0.720937i	$0.256288\pi$
$353$	−4.58761	+	20.0996i	−0.244174	+	1.06980i	−0.937175	+	0.348860i	$0.886569\pi$
$354$	0.628334	+	2.75291i	0.0333956	+	0.146316i
$355$	−1.95377	+	0.940887i	−0.103695	+	0.0499371i
$356$	−7.16637	+	8.98634i	−0.379817	+	0.476275i
$357$	0.110744	−	0.138869i	0.00586121	−	0.00734972i
$358$	−11.4242	−	5.50162i	−0.603789	−	0.290770i
$359$	13.0248	+	16.3325i	0.687420	+	0.861998i	0.996014	−	0.0891962i	$-0.0284298\pi$
$359$	13.0248	+	16.3325i	0.687420	+	0.861998i	−0.308594	+	0.951194i	$0.599858\pi$
$360$	0.533188			0.0281015
$361$	−10.7992	−	13.5418i	−0.568382	−	0.712728i
$362$	1.58761	+	6.95579i	0.0834431	+	0.365588i
$363$	−1.13826	−	4.98704i	−0.0597431	−	0.261752i
$364$	0.269946	+	0.338502i	0.0141490	+	0.0177423i
$365$	1.57434			0.0824045
$366$	−3.82640	−	4.79815i	−0.200009	−	0.250803i
$367$	−3.39008	−	1.63258i	−0.176961	−	0.0852199i	0.343306	−	0.939224i	$-0.388453\pi$
$367$	−3.39008	−	1.63258i	−0.176961	−	0.0852199i	−0.520267	+	0.854004i	$0.674168\pi$
$368$	4.85690	−	6.09035i	0.253183	−	0.317482i
$369$	−6.31551	+	7.91940i	−0.328772	+	0.412268i
$370$	−0.540188	+	0.260141i	−0.0280830	+	0.0135241i
$371$	−0.203866	−	0.893196i	−0.0105842	−	0.0463724i
$372$	−1.15399	+	5.05596i	−0.0598316	+	0.262139i
$373$	−13.5271	−	6.51433i	−0.700409	−	0.337299i	0.0495609	−	0.998771i	$-0.484218\pi$
$373$	−13.5271	−	6.51433i	−0.700409	−	0.337299i	−0.749970	+	0.661472i	$0.769932\pi$
$374$	3.50269	−	1.68681i	0.181120	−	0.0872227i
$375$	−0.243627	+	1.06740i	−0.0125809	+	0.0551203i
$376$	−0.801938			−0.0413568
$377$	12.5925	−	17.0700i	0.648545	−	0.879152i
$378$	−0.347207			−0.0178584
$379$	−5.24363	+	22.9738i	−0.269347	+	1.18009i	0.641428	+	0.767183i	$0.278342\pi$
$379$	−5.24363	+	22.9738i	−0.269347	+	1.18009i	−0.910775	+	0.412903i	$0.864515\pi$
$380$	−0.231250	+	0.111364i	−0.0118629	+	0.00571286i
$381$	−1.35421	−	0.652152i	−0.0693781	−	0.0334108i
$382$	0.711636	−	3.11788i	0.0364105	−	0.159525i
$383$	5.96830	+	26.1488i	0.304966	+	1.33614i	0.862528	+	0.506009i	$0.168880\pi$
$383$	5.96830	+	26.1488i	0.304966	+	1.33614i	−0.557562	+	0.830135i	$0.688263\pi$
$384$	−0.500000	+	0.240787i	−0.0255155	+	0.0122876i
$385$	−0.0181224	+	0.0227247i	−0.000923602	+	0.00115816i
$386$	9.39642	−	11.7827i	0.478265	−	0.599726i
$387$	−16.1652	−	7.78474i	−0.821722	−	0.395720i
$388$	−6.60388	−	8.28100i	−0.335261	−	0.420404i
$389$	−18.4034			−0.933090			−0.466545	−	0.884497i	$-0.654502\pi$
$389$	−18.4034			−0.933090			−0.466545	+	0.884497i	$0.654502\pi$
$390$	0.269946	+	0.338502i	0.0136693	+	0.0171407i
$391$	5.04743	+	22.1142i	0.255259	+	1.11836i
$392$	−1.55496	−	6.81272i	−0.0785372	−	0.344094i
$393$	5.05645	+	6.34059i	0.255064	+	0.319840i
$394$	14.5187			0.731442
$395$	0.603875	+	0.757236i	0.0303843	+	0.0381007i
$396$	−3.23825	−	1.55946i	−0.162728	−	0.0783658i
$397$	18.0233	−	22.6005i	0.904562	−	1.13428i	−0.0858736	−	0.996306i	$-0.527368\pi$
$397$	18.0233	−	22.6005i	0.904562	−	1.13428i	0.990435	−	0.137978i	$-0.0440604\pi$
$398$	−16.5402	+	20.7407i	−0.829085	+	1.03964i
$399$	0.0712201	−	0.0342978i	0.00356546	−	0.00171704i
$400$	1.10388	+	4.83639i	0.0551938	+	0.241820i
$401$	−3.41281	+	14.9525i	−0.170428	+	0.746693i	0.815395	+	0.578905i	$0.196520\pi$
$401$	−3.41281	+	14.9525i	−0.170428	+	0.746693i	−0.985823	+	0.167788i	$0.946338\pi$
$402$	5.50000	+	2.64866i	0.274315	+	0.132103i
$403$	33.1640	−	15.9709i	1.65202	−	0.795569i
$404$	−1.32908	+	5.82310i	−0.0661244	+	0.289710i
$405$	1.25236			0.0622301
$406$	0.523262	−	0.276700i	0.0259691	−	0.0137324i
$407$	4.04162			0.200336
$408$	0.359584	−	1.57544i	0.0178021	−	0.0779960i
$409$	31.2913	−	15.0691i	1.54726	−	0.745120i	0.551246	−	0.834343i	$-0.314153\pi$
$409$	31.2913	−	15.0691i	1.54726	−	0.745120i	0.996012	+	0.0892229i	$0.0284383\pi$
$410$	0.671448	+	0.323352i	0.0331604	+	0.0159692i
$411$	−0.196866	+	0.862525i	−0.00971067	+	0.0425452i
$412$	3.20291	+	14.0329i	0.157796	+	0.691349i
$413$	0.503885	−	0.242658i	0.0247946	−	0.0119404i
$414$	13.0749	−	16.3954i	0.642595	−	0.805788i
$415$	−1.44169	+	1.80782i	−0.0707698	+	0.0887425i
$416$	3.54892	+	1.70907i	0.174000	+	0.0837940i
$417$	−0.446534	−	0.559936i	−0.0218669	−	0.0274202i
$418$	1.73019			0.0846261
$419$	−13.6935	−	17.1711i	−0.668972	−	0.838864i	0.325315	−	0.945606i	$-0.394530\pi$
$419$	−13.6935	−	17.1711i	−0.668972	−	0.838864i	−0.994287	+	0.106742i	$0.965958\pi$
$420$	0.00268841	+	0.0117787i	0.000131181	+	0.000574740i
$421$	−8.99761	−	39.4211i	−0.438517	−	1.92127i	−0.385596	−	0.922668i	$-0.626004\pi$
$421$	−8.99761	−	39.4211i	−0.438517	−	1.92127i	−0.0529206	−	0.998599i	$-0.516853\pi$
$422$	10.4743	+	13.1344i	0.509883	+	0.639373i
$423$	−2.15883			−0.104966
$424$	−5.19687	−	6.51666i	−0.252382	−	0.316477i
$425$	−13.0145	−	6.26747i	−0.631298	−	0.304017i
$426$	3.78836	−	4.75046i	0.183547	−	0.230160i
$427$	−0.757865	+	0.950332i	−0.0366756	+	0.0459898i
$428$	14.8584	−	7.15542i	0.718207	−	0.345870i
$429$	−0.649440	−	2.84538i	−0.0313553	−	0.137376i
$430$	−0.293741	+	1.28696i	−0.0141654	+	0.0620629i
$431$	19.9121	+	9.58919i	0.959134	+	0.461895i	0.846880	−	0.531785i	$-0.178478\pi$
$431$	19.9121	+	9.58919i	0.959134	+	0.461895i	0.112255	+	0.993679i	$0.464193\pi$
$432$	−2.84601	+	1.37057i	−0.136929	+	0.0659414i
$433$	0.864961	−	3.78964i	0.0415674	−	0.182119i	−0.949882	−	0.312607i	$-0.898798\pi$
$433$	0.864961	−	3.78964i	0.0415674	−	0.182119i	0.991450	+	0.130489i	$0.0416547\pi$
$434$	1.02715			0.0493046
$435$	0.523262	−	0.276700i	0.0250885	−	0.0132667i
$436$	2.84117			0.136067
$437$	−2.24632	+	9.84175i	−0.107456	+	0.470795i
$438$	−3.97434	+	1.91394i	−0.189902	+	0.0914518i
$439$	−9.15160	−	4.40718i	−0.436782	−	0.210343i	0.202553	−	0.979271i	$-0.435076\pi$
$439$	−9.15160	−	4.40718i	−0.436782	−	0.210343i	−0.639335	+	0.768928i	$0.720790\pi$
$440$	−0.0588430	+	0.257808i	−0.00280523	+	0.0122905i
$441$	−4.18598	−	18.3400i	−0.199332	−	0.873332i
$442$	−10.3339	+	4.97656i	−0.491535	+	0.236711i
$443$	12.0312	−	15.0866i	0.571618	−	0.716786i	−0.409040	−	0.912516i	$-0.634136\pi$
$443$	12.0312	−	15.0866i	0.571618	−	0.716786i	0.980658	+	0.195730i	$0.0627078\pi$
$444$	1.04743	−	1.31343i	0.0497086	−	0.0623326i
$445$	2.05107	+	0.987745i	0.0972302	+	0.0468236i
$446$	0.893436	+	1.12033i	0.0423054	+	0.0530493i
$447$	3.71678			0.175797
$448$	0.0685317	+	0.0859360i	0.00323782	+	0.00406009i
$449$	−4.81522	−	21.0968i	−0.227244	−	0.995621i	−0.951876	−	0.306485i	$-0.900847\pi$
$449$	−4.81522	−	21.0968i	−0.227244	−	0.995621i	0.724631	−	0.689137i	$-0.242010\pi$
$450$	2.97166	+	13.0197i	0.140085	+	0.613753i
$451$	−3.13222	−	3.92768i	−0.147490	−	0.184947i
$452$	15.6746			0.737269
$453$	3.28501	+	4.11927i	0.154343	+	0.193540i
$454$	−12.0869	−	5.82077i	−0.567269	−	0.273182i
$455$	0.0534662	−	0.0670445i	0.00250653	−	0.00314309i
$456$	0.448394	−	0.562269i	0.0209980	−	0.0263306i
$457$	−2.28017	+	1.09807i	−0.106662	+	0.0513656i	−0.486454	−	0.873706i	$-0.661710\pi$
$457$	−2.28017	+	1.09807i	−0.106662	+	0.0513656i	0.379792	+	0.925072i	$0.375996\pi$
$458$	2.56100	+	11.2205i	0.119668	+	0.524298i
$459$	2.04676	−	8.96745i	0.0955346	−	0.418565i
$460$	−1.39008	−	0.669429i	−0.0648130	−	0.0312123i
$461$	−9.69687	+	4.66976i	−0.451628	+	0.217493i	−0.645849	−	0.763465i	$-0.723496\pi$
$461$	−9.69687	+	4.66976i	−0.451628	+	0.217493i	0.194221	+	0.980958i	$0.437782\pi$
$462$	0.0181224	−	0.0793993i	0.000843129	−	0.00369399i
$463$	−6.12392			−0.284603			−0.142301	−	0.989823i	$-0.545450\pi$
$463$	−6.12392			−0.284603			−0.142301	+	0.989823i	$0.545450\pi$
$464$	3.19687	−	4.33360i	0.148411	−	0.201182i
$465$	1.02715			0.0476328
$466$	−0.163678	+	0.717120i	−0.00758223	+	0.0332199i
$467$	−31.5013	+	15.1702i	−1.45770	+	0.701993i	−0.983914	−	0.178644i	$-0.942829\pi$
$467$	−31.5013	+	15.1702i	−1.45770	+	0.701993i	−0.473790	+	0.880638i	$0.657115\pi$
$468$	9.55376	+	4.60085i	0.441623	+	0.212674i
$469$	0.269045	−	1.17876i	0.0124234	−	0.0544303i
$470$	0.0353438	+	0.154851i	0.00163029	+	0.00714276i
$471$	4.69687	−	2.26189i	0.216420	−	0.104222i
$472$	3.17241	−	3.97807i	0.146022	−	0.183106i
$473$	5.54809	−	6.95708i	0.255101	−	0.319887i
$474$	−2.44504	−	1.17747i	−0.112304	−	0.0540830i
$475$	−4.00820	−	5.02612i	−0.183909	−	0.230614i
$476$	−0.320060			−0.0146699
$477$	−13.9901	−	17.5430i	−0.640562	−	0.803239i
$478$	0.0196143	+	0.0859360i	0.000897139	+	0.00393062i
$479$	6.86994	+	30.0992i	0.313895	+	1.37527i	0.848067	+	0.529889i	$0.177767\pi$
$479$	6.86994	+	30.0992i	0.313895	+	1.37527i	−0.534171	+	0.845376i	$0.679376\pi$
$480$	0.0685317	+	0.0859360i	0.00312803	+	0.00392242i
$481$	−11.9239			−0.543685
$482$	3.87382	+	4.85762i	0.176448	+	0.221258i
$483$	0.428116	+	0.206170i	0.0194799	+	0.00938105i
$484$	−5.74698	+	7.20648i	−0.261226	+	0.327567i
$485$	−1.30798	+	1.64015i	−0.0593922	+	0.0744755i
$486$	−11.6996	+	5.63421i	−0.530703	+	0.255573i
$487$	0.0908344	+	0.397972i	0.00411610	+	0.0180338i	0.976944	−	0.213495i	$-0.0684845\pi$
$487$	0.0908344	+	0.397972i	0.00411610	+	0.0180338i	−0.972828	+	0.231528i	$0.925627\pi$
$488$	−2.46077	+	10.7813i	−0.111394	+	0.488048i
$489$	−8.13437	−	3.91731i	−0.367849	−	0.177147i
$490$	−1.24698	+	0.600514i	−0.0563328	+	0.0271284i
$491$	−4.48643	+	19.6563i	−0.202470	+	0.887077i	0.766958	+	0.641698i	$0.221770\pi$
$491$	−4.48643	+	19.6563i	−0.202470	+	0.887077i	−0.969427	+	0.245379i	$0.921087\pi$
$492$	−2.08815			−0.0941409
$493$	4.06183	+	15.1456i	0.182935	+	0.682124i
$494$	−5.10454			−0.229664
$495$	−0.158407	+	0.694025i	−0.00711985	+	0.0311941i
$496$	8.41939	−	4.05456i	0.378042	−	0.182055i
$497$	−1.08426	−	0.522153i	−0.0486358	−	0.0234217i
$498$	1.44169	−	6.31645i	0.0646037	−	0.283047i
$499$	2.30947	+	10.1185i	0.103386	+	0.452964i	0.999950	+	0.0100487i	$0.00319865\pi$
$499$	2.30947	+	10.1185i	0.103386	+	0.452964i	−0.896563	+	0.442915i	$0.853944\pi$
$500$	1.77748	−	0.855989i	0.0794913	−	0.0382810i
$501$	4.76205	−	5.97142i	0.212752	−	0.266783i
$502$	−9.47166	+	11.8771i	−0.422741	+	0.530100i
$503$	−20.7141	−	9.97538i	−0.923596	−	0.444780i	−0.0892420	−	0.996010i	$-0.528444\pi$
$503$	−20.7141	−	9.97538i	−0.923596	−	0.444780i	−0.834353	+	0.551230i	$0.814159\pi$
$504$	0.184489	+	0.231342i	0.00821778	+	0.0103048i
$505$	1.18300			0.0526427
$506$	6.48457	+	8.13139i	0.288274	+	0.361484i
$507$	0.310667	+	1.36112i	0.0137972	+	0.0604495i
$508$	0.602679	+	2.64051i	0.0267396	+	0.117154i
$509$	16.0262	+	20.0963i	0.710351	+	0.890752i	0.997749	−	0.0670594i	$-0.0213617\pi$
$509$	16.0262	+	20.0963i	0.710351	+	0.890752i	−0.287398	+	0.957811i	$0.592790\pi$
$510$	−0.320060			−0.0141725
$511$	0.544737	+	0.683079i	0.0240977	+	0.0302176i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$	2.55227	−	3.20045i	0.112685	−	0.141303i
$514$	−3.44839	+	4.32415i	−0.152102	+	0.190730i
$515$	2.56853	−	1.23694i	0.113183	−	0.0545061i
$516$	−0.823044	−	3.60599i	−0.0362325	−	0.158745i
$517$	0.238250	−	1.04384i	0.0104782	−	0.0459082i
$518$	−0.299782	−	0.144367i	−0.0131717	−	0.00634314i
$519$	−0.0598025	+	0.0287994i	−0.00262504	+	0.00126415i
$520$	0.173604	−	0.760607i	0.00761302	−	0.0333548i
$521$	17.1535			0.751507			0.375753	−	0.926720i	$-0.377384\pi$
$521$	17.1535			0.751507			0.375753	+	0.926720i	$0.377384\pi$
$522$	8.60603	−	11.6661i	0.376676	−	0.510613i
$523$	22.4494			0.981642			0.490821	−	0.871261i	$-0.336697\pi$
$523$	22.4494			0.981642			0.490821	+	0.871261i	$0.336697\pi$
$524$	3.25182	−	14.2472i	0.142057	−	0.622391i
$525$	−0.272635	+	0.131294i	−0.0118988	+	0.00573014i
$526$	1.97166	+	0.949500i	0.0859683	+	0.0414002i
$527$	−6.05496	+	26.5285i	−0.263758	+	1.15560i
$528$	−0.164874	−	0.722362i	−0.00717524	−	0.0314368i
$529$	−33.9502	+	16.3495i	−1.47609	+	0.710850i
$530$	−1.02930	+	1.29071i	−0.0447101	+	0.0560646i
$531$	8.54019	−	10.7091i	0.370613	−	0.464733i
$532$	−0.128334	−	0.0618025i	−0.00556399	−	0.00267948i
$533$	9.24094	+	11.5878i	0.400269	+	0.501922i
$534$	−6.37867			−0.276032
$535$	−2.03654	−	2.55374i	−0.0880473	−	0.110408i
$536$	−2.44773	−	10.7242i	−0.105726	−	0.463215i
$537$	−1.56584	−	6.86041i	−0.0675711	−	0.296048i
$538$	−18.9901	−	23.8128i	−0.818720	−	1.02664i
$539$	9.32975			0.401861
$540$	0.390084	+	0.489150i	0.0167865	+	0.0210496i
$541$	11.2104	+	5.39866i	0.481974	+	0.232107i	0.659062	−	0.752088i	$-0.270953\pi$
$541$	11.2104	+	5.39866i	0.481974	+	0.232107i	−0.177088	+	0.984195i	$0.556668\pi$
$542$	−19.6685	+	24.6635i	−0.844835	+	1.05939i
$543$	−2.46867	+	3.09562i	−0.105941	+	0.132846i
$544$	−2.62349	+	1.26341i	−0.112481	+	0.0541681i
$545$	−0.125219	−	0.548619i	−0.00536378	−	0.0235003i
$546$	−0.0534662	+	0.234251i	−0.00228814	+	0.0100250i
$547$	10.5988	+	5.10411i	0.453172	+	0.218236i	0.646524	−	0.762893i	$-0.276222\pi$
$547$	10.5988	+	5.10411i	0.453172	+	0.218236i	−0.193353	+	0.981129i	$0.561936\pi$
$548$	1.43631	−	0.691692i	0.0613562	−	0.0295476i
$549$	−6.62445	+	29.0236i	−0.282725	+	1.23870i
$550$	−6.62325			−0.282416
$551$	−1.29590	+	6.85724i	−0.0552071	+	0.292128i
$552$	4.32304			0.184001
$553$	−0.119605	+	0.524023i	−0.00508612	+	0.0222837i
$554$	12.7959	−	6.16218i	0.543646	−	0.261806i
$555$	−0.299782	−	0.144367i	−0.0127250	−	0.00612805i
$556$	−0.287168	+	1.25816i	−0.0121786	+	0.0533580i
$557$	−7.28448	−	31.9154i	−0.308653	−	1.35230i	−0.856685	−	0.515841i	$-0.827480\pi$
$557$	−7.28448	−	31.9154i	−0.308653	−	1.35230i	0.548031	−	0.836458i	$-0.315377\pi$
$558$	22.6652	−	10.9150i	0.959493	−	0.462068i
$559$	−16.3684	+	20.5254i	−0.692311	+	0.868131i
$560$	0.0135735	−	0.0170207i	0.000573587	−	0.000719255i
$561$	1.94385	+	0.936107i	0.0820692	+	0.0395225i
$562$	−12.9453	−	16.2329i	−0.546066	−	0.684745i
$563$	−30.1105			−1.26901			−0.634503	−	0.772920i	$-0.718795\pi$
$563$	−30.1105			−1.26901			−0.634503	+	0.772920i	$0.718795\pi$
$564$	−0.277479	−	0.347948i	−0.0116840	−	0.0146512i
$565$	−0.690825	−	3.02670i	−0.0290632	−	0.127334i
$566$	−3.86012	−	16.9123i	−0.162253	−	0.710876i
$567$	0.433329	+	0.543377i	0.0181981	+	0.0228197i
$568$	−10.9487			−0.459397
$569$	9.71230	+	12.1788i	0.407161	+	0.510563i	0.942561	−	0.334035i	$-0.108410\pi$
$569$	9.71230	+	12.1788i	0.407161	+	0.510563i	−0.535400	+	0.844599i	$0.679839\pi$
$570$	−0.128334	−	0.0618025i	−0.00537533	−	0.00258862i
$571$	4.20589	−	5.27402i	0.176011	−	0.220711i	−0.685998	−	0.727603i	$-0.740634\pi$
$571$	4.20589	−	5.27402i	0.176011	−	0.220711i	0.862009	+	0.506892i	$0.169206\pi$
$572$	−3.27897	+	4.11170i	−0.137101	+	0.171919i
$573$	1.59903	−	0.770053i	0.0668005	−	0.0321694i
$574$	0.0920309	+	0.403214i	0.00384129	+	0.0168298i
$575$	8.59903	−	37.6748i	0.358604	−	1.57115i
$576$	2.42543	+	1.16802i	0.101059	+	0.0486677i
$577$	16.8458	−	8.11250i	0.701299	−	0.337728i	−0.0490256	−	0.998798i	$-0.515612\pi$
$577$	16.8458	−	8.11250i	0.701299	−	0.337728i	0.750324	+	0.661070i	$0.229897\pi$
$578$	−1.89612	+	8.30746i	−0.0788684	+	0.345545i
$579$	8.36360			0.347579
$580$	−0.977697	−	0.426309i	−0.0405967	−	0.0177015i
$581$	−1.28322			−0.0532371
$582$	1.30798	−	5.73063i	0.0542175	−	0.237542i
$583$	10.0264	−	4.82845i	0.415250	−	0.199974i
$584$	7.16152	+	3.44881i	0.296346	+	0.142713i
$585$	0.467345	−	2.04757i	0.0193223	−	0.0846566i
$586$	3.90030	+	17.0884i	0.161120	+	0.705913i
$587$	14.6407	−	7.05059i	0.604287	−	0.291009i	−0.106615	−	0.994300i	$-0.534001\pi$
$587$	14.6407	−	7.05059i	0.604287	−	0.291009i	0.710902	+	0.703291i	$0.248287\pi$
$588$	2.41789	−	3.03194i	0.0997123	−	0.125035i
$589$	−7.55041	+	9.46791i	−0.311109	+	0.390119i
$590$	−0.907969	−	0.437255i	−0.0373805	−	0.0180015i
$591$	5.02363	+	6.29943i	0.206645	+	0.259124i
$592$	−3.02715			−0.124415
$593$	19.4351	+	24.3709i	0.798105	+	1.00079i	0.999772	+	0.0213375i	$0.00679245\pi$
$593$	19.4351	+	24.3709i	0.798105	+	1.00079i	−0.201668	+	0.979454i	$0.564636\pi$
$594$	−0.938469	−	4.11170i	−0.0385058	−	0.168705i
$595$	0.0141060	+	0.0618025i	0.000578290	+	0.00253365i
$596$	−4.17576	−	5.23624i	−0.171046	−	0.214485i
$597$	−14.7222			−0.602538
$598$	−19.1313	−	23.9899i	−0.782338	−	0.981021i
$599$	−7.05280	−	3.39645i	−0.288170	−	0.138775i	0.284215	−	0.958761i	$-0.408267\pi$
$599$	−7.05280	−	3.39645i	−0.288170	−	0.138775i	−0.572384	+	0.819985i	$0.693981\pi$
$600$	−1.71648	+	2.15240i	−0.0700750	+	0.0878713i
$601$	10.9566	−	13.7391i	0.446929	−	0.560431i	−0.506426	−	0.862283i	$-0.669034\pi$
$601$	10.9566	−	13.7391i	0.446929	−	0.560431i	0.953355	+	0.301853i	$0.0976051\pi$
$602$	−0.660030	+	0.317854i	−0.0269008	+	0.0129548i
$603$	−6.58934	−	28.8698i	−0.268339	−	1.17567i
$604$	2.11260	−	9.25593i	0.0859607	−	0.376618i
$605$	1.64483	+	0.792110i	0.0668720	+	0.0322038i
$606$	−2.98643	+	1.43819i	−0.121315	+	0.0584224i
$607$	8.75504	−	38.3584i	0.355356	−	1.55692i	−0.409251	−	0.912422i	$-0.634210\pi$
$607$	8.75504	−	38.3584i	0.355356	−	1.55692i	0.764608	−	0.644496i	$-0.222933\pi$
$608$	−1.29590			−0.0525556
$609$	0.301110	+	0.131294i	0.0122016	+	0.00532030i
$610$	2.19029			0.0886824
$611$	−0.702907	+	3.07964i	−0.0284366	+	0.124589i
$612$	−7.06249	+	3.40112i	−0.285484	+	0.137482i
$613$	−22.6429	−	10.9042i	−0.914537	−	0.440418i	−0.0834193	−	0.996515i	$-0.526584\pi$
$613$	−22.6429	−	10.9042i	−0.914537	−	0.440418i	−0.831118	+	0.556097i	$0.812298\pi$
$614$	6.75614	−	29.6006i	0.272655	−	1.19458i
$615$	0.0920309	+	0.403214i	0.00371104	+	0.0162591i
$616$	−0.132219	+	0.0636733i	−0.00532726	+	0.00256547i
$617$	−7.87047	+	9.86926i	−0.316853	+	0.397321i	−0.914597	−	0.404366i	$-0.867492\pi$
$617$	−7.87047	+	9.86926i	−0.316853	+	0.397321i	0.597744	+	0.801687i	$0.296064\pi$
$618$	−4.98039	+	6.24521i	−0.200340	+	0.251219i
$619$	19.5683	+	9.42359i	0.786516	+	0.378766i	0.783629	−	0.621230i	$-0.213367\pi$
$619$	19.5683	+	9.42359i	0.786516	+	0.378766i	0.00288757	+	0.999996i	$0.499081\pi$
$620$	−1.15399	−	1.44706i	−0.0463453	−	0.0581152i
$621$	24.6069			0.987439
$622$	14.8312	+	18.5978i	0.594679	+	0.745703i
$623$	0.281127	+	1.23170i	0.0112631	+	0.0493469i
$624$	0.486426	+	2.13117i	0.0194726	+	0.0853152i
$625$	15.2213	+	19.0869i	0.608853	+	0.763477i
$626$	28.6746			1.14607
$627$	0.598663	+	0.750699i	0.0239083	+	0.0299800i
$628$	−8.46346	−	4.07579i	−0.337729	−	0.162642i
$629$	5.49582	−	6.89154i	0.219133	−	0.274784i
$630$	0.0365403	−	0.0458200i	0.00145580	−	0.00182551i
$631$	35.4616	−	17.0774i	1.41170	−	0.679841i	0.436206	−	0.899847i	$-0.356322\pi$
$631$	35.4616	−	17.0774i	1.41170	−	0.679841i	0.975498	+	0.220006i	$0.0706078\pi$
$632$	1.08815	+	4.76748i	0.0432841	+	0.189640i
$633$	−2.07457	+	9.08930i	−0.0824569	+	0.361267i
$634$	−6.80947	−	3.27927i	−0.270439	−	0.130236i
$635$	0.483311	−	0.232750i	0.0191796	−	0.00923642i
$636$	1.02930	−	4.50967i	0.0408145	−	0.178820i
$637$	−27.5254			−1.09060
$638$	4.69106	+	5.44869i	0.185721	+	0.215716i
$639$	−29.4741			−1.16598
$640$	0.0440730	−	0.193096i	0.00174214	−	0.00763281i
$641$	4.44020	−	2.13829i	0.175377	−	0.0844572i	−0.344135	−	0.938920i	$-0.611828\pi$
$641$	4.44020	−	2.13829i	0.175377	−	0.0844572i	0.519512	+	0.854463i	$0.326114\pi$
$642$	8.24578	+	3.97096i	0.325435	+	0.156721i
$643$	1.56004	−	6.83498i	0.0615220	−	0.269545i	−0.934807	−	0.355157i	$-0.884427\pi$
$643$	1.56004	−	6.83498i	0.0615220	−	0.269545i	0.996329	+	0.0856119i	$0.0272845\pi$
$644$	−0.190530	−	0.834764i	−0.00750791	−	0.0328943i
$645$	−0.660030	+	0.317854i	−0.0259887	+	0.0125155i
$646$	2.35272	−	2.95021i	0.0925664	−	0.116075i
$647$	−9.18329	+	11.5155i	−0.361032	+	0.452720i	−0.928862	−	0.370426i	$-0.879212\pi$
$647$	−9.18329	+	11.5155i	−0.361032	+	0.452720i	0.567830	+	0.823146i	$0.307783\pi$
$648$	5.69687	+	2.74347i	0.223794	+	0.107774i
$649$	4.23556	+	5.31123i	0.166260	+	0.208484i
$650$	19.5405			0.766441
$651$	0.355404	+	0.445662i	0.0139294	+	0.0174669i
$652$	3.62014	+	15.8609i	0.141776	+	0.621159i
$653$	5.56691	+	24.3902i	0.217850	+	0.954463i	0.959063	+	0.283193i	$0.0913937\pi$
$653$	5.56691	+	24.3902i	0.217850	+	0.954463i	−0.741213	+	0.671270i	$0.765749\pi$
$654$	0.983074	+	1.23274i	0.0384412	+	0.0482038i
$655$	−2.89440			−0.113093
$656$	2.34601	+	2.94180i	0.0915963	+	0.114858i
$657$	19.2790	+	9.28426i	0.752144	+	0.362214i
$658$	−0.0549581	+	0.0689153i	−0.00214249	+	0.00268660i
$659$	30.3384	−	38.0432i	1.18182	−	1.48195i	0.341477	−	0.939890i	$-0.389073\pi$
$659$	30.3384	−	38.0432i	1.18182	−	1.48195i	0.840339	−	0.542061i	$-0.182356\pi$
$660$	−0.132219	+	0.0636733i	−0.00514662	+	0.00247848i
$661$	6.40528	+	28.0634i	0.249137	+	1.09154i	0.932417	+	0.361383i	$0.117695\pi$
$661$	6.40528	+	28.0634i	0.249137	+	1.09154i	−0.683281	+	0.730156i	$0.739448\pi$
$662$	−2.48911	+	10.9055i	−0.0967422	+	0.423855i
$663$	−5.73490	−	2.76178i	−0.222725	−	0.107259i
$664$	−10.5184	+	5.06540i	−0.408194	+	0.196576i
$665$	−0.00627776	+	0.0275047i	−0.000243441	+	0.00106659i
$666$	−8.14914			−0.315773
$667$	−37.0840	+	19.6099i	−1.43590	+	0.759299i
$668$	−13.7627			−0.532495
$669$	−0.176956	+	0.775295i	−0.00684151	+	0.0299746i
$670$	−1.96293	+	0.945296i	−0.0758345	+	0.0365200i
$671$	−13.3025	−	6.40613i	−0.513536	−	0.247306i
$672$	−0.0135735	+	0.0594696i	−0.000523611	+	0.00229409i
$673$	−5.14782	−	22.5541i	−0.198434	−	0.869395i	−0.971869	−	0.235520i	$-0.924321\pi$
$673$	−5.14782	−	22.5541i	−0.198434	−	0.869395i	0.773436	−	0.633875i	$-0.218537\pi$
$674$	−18.7337	+	9.02168i	−0.721595	+	0.347502i
$675$	−9.77024	+	12.2515i	−0.376057	+	0.471560i
$676$	1.56853	−	1.96688i	0.0603281	−	0.0756491i
$677$	16.2690	+	7.83476i	0.625270	+	0.301114i	0.719560	−	0.694431i	$-0.244344\pi$
$677$	16.2690	+	7.83476i	0.625270	+	0.301114i	−0.0942895	+	0.995545i	$0.530058\pi$
$678$	5.42357	+	6.80094i	0.208291	+	0.261188i
$679$	−1.16421			−0.0446783
$680$	0.359584	+	0.450904i	0.0137894	+	0.0172914i
$681$	−1.65668	−	7.25838i	−0.0634840	−	0.278142i
$682$	2.77628	+	12.1637i	0.106309	+	0.465772i
$683$	−27.5127	−	34.4998i	−1.05274	−	1.32010i	−0.945413	−	0.325875i	$-0.894341\pi$
$683$	−27.5127	−	34.4998i	−1.05274	−	1.32010i	−0.107330	−	0.994223i	$-0.534230\pi$
$684$	−3.48858			−0.133389
$685$	−0.196866	−	0.246862i	−0.00752186	−	0.00943211i
$686$	−1.38524	−	0.667096i	−0.0528887	−	0.0254698i
$687$	−3.98225	+	4.99358i	−0.151932	+	0.190517i
$688$	−4.15548	+	5.21081i	−0.158426	+	0.198660i
$689$	−29.5807	+	14.2453i	−1.12693	+	0.542703i
$690$	−0.190530	−	0.834764i	−0.00725333	−	0.0317789i
$691$	−5.30702	+	23.2516i	−0.201889	+	0.884531i	0.767897	+	0.640573i	$0.221303\pi$
$691$	−5.30702	+	23.2516i	−0.201889	+	0.884531i	−0.969786	+	0.243958i	$0.921554\pi$
$692$	0.107760	+	0.0518946i	0.00409643	+	0.00197274i
$693$	−0.355936	+	0.171410i	−0.0135209	+	0.00651132i
$694$	0.00431187	−	0.0188915i	0.000163676	−	0.000717113i
$695$	0.255603			0.00969559
$696$	2.98643	−	0.112402i	0.113200	−	0.00426060i
$697$	−10.9565			−0.415005
$698$	6.46011	−	28.3036i	0.244519	−	1.07131i
$699$	−0.367781	+	0.177114i	−0.0139108	+	0.00669907i
$700$	0.491271	+	0.236584i	0.0185683	+	0.00894202i
$701$	−0.249668	+	1.09387i	−0.00942983	+	0.0413148i	−0.979424	−	0.201814i	$-0.935316\pi$
$701$	−0.249668	+	1.09387i	−0.00942983	+	0.0413148i	0.969994	+	0.243128i	$0.0781736\pi$
$702$	2.76875	+	12.1307i	0.104500	+	0.457843i
$703$	3.53438	−	1.70207i	0.133302	−	0.0641948i
$704$	−0.832437	+	1.04384i	−0.0313737	+	0.0393413i
$705$	−0.0549581	+	0.0689153i	−0.00206984	+	0.00259550i
$706$	18.5749	+	8.94518i	0.699074	+	0.336656i
$707$	0.409330	+	0.513283i	0.0153944	+	0.0193040i
$708$	2.82371			0.106121
$709$	2.54623	+	3.19287i	0.0956256	+	0.119911i	0.827342	−	0.561698i	$-0.189852\pi$
$709$	2.54623	+	3.19287i	0.0956256	+	0.119911i	−0.731716	+	0.681609i	$0.761280\pi$
$710$	0.482542	+	2.11415i	0.0181095	+	0.0793427i
$711$	2.92931	+	12.8342i	0.109858	+	0.481318i
$712$	7.16637	+	8.98634i	0.268571	+	0.336777i
$713$	−72.7948			−2.72619
$714$	−0.110744	−	0.138869i	−0.00414450	−	0.00519704i
$715$	0.938469	+	0.451943i	0.0350967	+	0.0169017i
$716$	−7.90581	+	9.91358i	−0.295454	+	0.370488i
$717$	−0.0304995	+	0.0382451i	−0.00113902	+	0.00142829i
$718$	18.8213	−	9.06387i	0.702405	−	0.338261i
$719$	−6.48062	−	28.3935i	−0.241686	−	1.05890i	−0.939481	−	0.342600i	$-0.888692\pi$
$719$	−6.48062	−	28.3935i	−0.241686	−	1.05890i	0.697795	−	0.716298i	$-0.254165\pi$
$720$	0.118645	−	0.519820i	0.00442166	−	0.0193725i
$721$	1.42543	+	0.686450i	0.0530857	+	0.0255647i
$722$	−15.6054	+	7.51515i	−0.580772	+	0.279685i
$723$	−0.767258	+	3.36158i	−0.0285346	+	0.125018i
$724$	7.13467			0.265158
$725$	4.96077	−	26.2499i	0.184238	−	0.974898i
$726$	−5.11529			−0.189846
$727$	3.52888	−	15.4610i	0.130879	−	0.573417i	−0.866377	−	0.499390i	$-0.833558\pi$
$727$	3.52888	−	15.4610i	0.130879	−	0.573417i	0.997256	−	0.0740276i	$-0.0235853\pi$
$728$	0.390084	−	0.187854i	0.0144575	−	0.00696235i
$729$	10.5978	+	5.10365i	0.392512	+	0.189024i
$730$	0.350323	−	1.53486i	0.0129660	−	0.0568079i
$731$	−4.31850	−	18.9206i	−0.159725	−	0.699802i
$732$	−5.52930	+	2.66277i	−0.204369	+	0.0984189i
$733$	−13.3490	+	16.7391i	−0.493056	+	0.618273i	−0.964647	−	0.263544i	$-0.915108\pi$
$733$	−13.3490	+	16.7391i	−0.493056	+	0.618273i	0.471591	+	0.881817i	$0.343680\pi$
$734$	−2.34601	+	2.94180i	−0.0865928	+	0.108584i
$735$	−0.692021	−	0.333260i	−0.0255256	−	0.0122925i
$736$	−4.85690	−	6.09035i	−0.179028	−	0.224493i
$737$	14.6864			0.540980
$738$	6.31551	+	7.91940i	0.232477	+	0.291517i
$739$	7.48547	+	32.7960i	0.275357	+	1.20642i	0.903592	+	0.428395i	$0.140921\pi$
$739$	7.48547	+	32.7960i	0.275357	+	1.20642i	−0.628234	+	0.778024i	$0.716222\pi$
$740$	0.133415	+	0.584531i	0.00490445	+	0.0214878i
$741$	−1.76623	−	2.21478i	−0.0648839	−	0.0813619i
$742$	−0.916166			−0.0336335
$743$	3.38972	+	4.25057i	0.124357	+	0.155938i	0.840112	−	0.542413i	$-0.182489\pi$
$743$	3.38972	+	4.25057i	0.124357	+	0.155938i	−0.715756	+	0.698351i	$0.753918\pi$
$744$	4.67241	+	2.25011i	0.171299	+	0.0824931i
$745$	−0.827060	+	1.03710i	−0.0303011	+	0.0379964i
$746$	−9.36108	+	11.7384i	−0.342733	+	0.429774i
$747$	−28.3158	+	13.6362i	−1.03602	+	0.498922i
$748$	−0.865093	−	3.79022i	−0.0316309	−	0.138584i
$749$	0.403362	−	1.76724i	0.0147385	−	0.0645737i
$750$	0.986426	+	0.475038i	0.0360192	+	0.0173459i
$751$	15.1341	−	7.28822i	0.552253	−	0.265951i	−0.136878	−	0.990588i	$-0.543707\pi$
$751$	15.1341	−	7.28822i	0.552253	−	0.265951i	0.689131	+	0.724637i	$0.257993\pi$
$752$	−0.178448	+	0.781831i	−0.00650733	+	0.0285105i
$753$	−8.43057			−0.307227
$754$	−13.8400	−	16.0752i	−0.504022	−	0.585423i
$755$	−1.88040			−0.0684346
$756$	−0.0772609	+	0.338502i	−0.00280995	+	0.0123112i
$757$	−2.26271	+	1.08966i	−0.0822396	+	0.0396045i	−0.474551	−	0.880228i	$-0.657390\pi$
$757$	−2.26271	+	1.08966i	−0.0822396	+	0.0396045i	0.392312	+	0.919832i	$0.371675\pi$
$758$	21.2310	+	10.2243i	0.771145	+	0.371364i
$759$	−1.28435	+	5.62710i	−0.0466189	+	0.204251i
$760$	0.0571141	+	0.250233i	0.00207174	+	0.00907691i
$761$	48.2367	−	23.2296i	1.74858	−	0.842071i	0.769484	−	0.638666i	$-0.220514\pi$
$761$	48.2367	−	23.2296i	1.74858	−	0.842071i	0.979095	−	0.203405i	$-0.0652007\pi$
$762$	−0.937141	+	1.17514i	−0.0339490	+	0.0425707i
$763$	0.194710	−	0.244158i	0.00704897	−	0.00883913i
$764$	−2.88135	−	1.38759i	−0.104244	−	0.0502011i
$765$	0.968009	+	1.21384i	0.0349984	+	0.0438866i
$766$	26.8213			0.969094
$767$	−12.4961	−	15.6696i	−0.451209	−	0.565798i
$768$	0.123490	+	0.541044i	0.00445605	+	0.0195232i
$769$	−2.05658	−	9.01047i	−0.0741622	−	0.324926i	0.924215	−	0.381873i	$-0.124721\pi$
$769$	−2.05658	−	9.01047i	−0.0741622	−	0.324926i	−0.998377	+	0.0569466i	$0.981864\pi$
$770$	0.0181224	+	0.0227247i	0.000653085	+	0.000818943i
$771$	−3.06936			−0.110540
$772$	−9.39642	−	11.7827i	−0.338185	−	0.424070i
$773$	33.7298	+	16.2434i	1.21318	+	0.584235i	0.927404	−	0.374062i	$-0.122035\pi$
$773$	33.7298	+	16.2434i	1.21318	+	0.584235i	0.285773	+	0.958297i	$0.407750\pi$
$774$	−11.1866	+	14.0276i	−0.402096	+	0.504212i
$775$	28.9034	−	36.2437i	1.03824	−	1.30191i
$776$	−9.54288	+	4.59561i	−0.342569	+	0.164973i
$777$	−0.0410891	−	0.180023i	−0.00147406	−	0.00645829i
$778$	−4.09515	+	17.9420i	−0.146818	+	0.643252i
$779$	−4.39320	−	2.11565i	−0.157403	−	0.0758011i
$780$	0.390084	−	0.187854i	0.0139672	−	0.00672627i
$781$	3.25278	−	14.2514i	0.116394	−	0.509954i
$782$	22.6829			0.811140
$783$	16.9988	−	0.639797i	0.607488	−	0.0228645i
$784$	−6.98792			−0.249569
$785$	−0.414010	+	1.81390i	−0.0147766	+	0.0647407i
$786$	7.30678	−	3.51876i	0.260624	−	0.125510i
$787$	−23.3686	−	11.2537i	−0.833001	−	0.401152i	−0.0317612	−	0.999495i	$-0.510112\pi$
$787$	−23.3686	−	11.2537i	−0.833001	−	0.401152i	−0.801240	+	0.598343i	$0.795826\pi$
$788$	3.23072	−	14.1547i	0.115090	−	0.504240i
$789$	0.270242	+	1.18401i	0.00962086	+	0.0421518i
$790$	0.872625	−	0.420234i	0.0310466	−	0.0149513i
$791$	1.07420	−	1.34701i	0.0381943	−	0.0478941i
$792$	−2.24094	+	2.81005i	−0.0796283	+	0.0998507i
$793$	39.2461	+	18.8999i	1.39367	+	0.671156i
$794$	−18.0233	−	22.6005i	−0.639622	−	0.802060i
$795$	−0.916166			−0.0324931
$796$	16.5402	+	20.7407i	0.586251	+	0.735136i
$797$	−4.49300	−	19.6851i	−0.159150	−	0.697283i	−0.990033	−	0.140835i	$-0.955021\pi$
$797$	−4.49300	−	19.6851i	−0.159150	−	0.697283i	0.830883	−	0.556447i	$-0.187836\pi$
$798$	−0.0175899	−	0.0770664i	−0.000622676	−	0.00272812i
$799$	−1.45593	−	1.82567i	−0.0515070	−	0.0645877i
$800$	4.96077			0.175390
$801$	19.2920	+	24.1914i	0.681650	+	0.854762i
$802$	13.8182	+	6.65449i	0.487938	+	0.234978i
$803$	−6.61679	+	8.29719i	−0.233501	+	0.292801i
$804$	3.80612	−	4.77272i	0.134231	−	0.168321i
$805$	−0.152793	+	0.0735811i	−0.00538524	+	0.00259339i
$806$	−8.19083	−	35.8863i	−0.288510	−	1.26404i
$807$	3.76122	−	16.4790i	0.132401	−	0.580087i
$808$	5.38135	+	2.59152i	0.189315	+	0.0911695i
$809$	−31.0306	+	14.9435i	−1.09098	+	0.525387i	−0.890810	−	0.454375i	$-0.849862\pi$
$809$	−31.0306	+	14.9435i	−1.09098	+	0.525387i	−0.200166	+	0.979762i	$0.564148\pi$
$810$	0.278676	−	1.22096i	0.00979166	−	0.0429001i
$811$	32.7536			1.15013			0.575067	−	0.818106i	$-0.304976\pi$
$811$	32.7536			1.15013			0.575067	+	0.818106i	$0.304976\pi$
$812$	−0.153325	−	0.571714i	−0.00538066	−	0.0200632i
$813$	−17.5066			−0.613984
$814$	0.899345	−	3.94029i	0.0315220	−	0.138107i
$815$	2.90312	−	1.39807i	0.101692	−	0.0489723i
$816$	−1.45593	−	0.701137i	−0.0509676	−	0.0245447i
$817$	1.92191	−	8.42044i	0.0672392	−	0.294594i
$818$	−7.72832	−	33.8600i	−0.270215	−	1.18389i
$819$	1.05011	−	0.505708i	0.0366939	−	0.0176709i
$820$	0.464656	−	0.582660i	0.0162265	−	0.0203474i
$821$	2.70978	−	3.39795i	0.0945718	−	0.118589i	−0.732294	−	0.680989i	$-0.761550\pi$
$821$	2.70978	−	3.39795i	0.0945718	−	0.118589i	0.826866	+	0.562399i	$0.190122\pi$
$822$	0.797093	+	0.383860i	0.0278018	+	0.0133887i
$823$	8.36108	+	10.4845i	0.291449	+	0.365465i	0.905902	−	0.423488i	$-0.139195\pi$
$823$	8.36108	+	10.4845i	0.291449	+	0.365465i	−0.614453	+	0.788954i	$0.710623\pi$
$824$	14.3937			0.501429
$825$	−2.29172	−	2.87372i	−0.0797873	−	0.100050i
$826$	−0.124449	−	0.545248i	−0.00433014	−	0.0189716i
$827$	5.86174	+	25.6820i	0.203833	+	0.893049i	0.968577	+	0.248715i	$0.0800083\pi$
$827$	5.86174	+	25.6820i	0.203833	+	0.893049i	−0.764744	+	0.644334i	$0.777135\pi$
$828$	−13.0749	−	16.3954i	−0.454383	−	0.569778i
$829$	−10.3618			−0.359880			−0.179940	−	0.983678i	$-0.557590\pi$
$829$	−10.3618			−0.359880			−0.179940	+	0.983678i	$0.557590\pi$
$830$	1.44169	+	1.80782i	0.0500418	+	0.0627504i
$831$	7.10119	+	3.41975i	0.246337	+	0.118630i
$832$	2.45593	−	3.07964i	0.0851439	−	0.106767i
$833$	12.6866	−	15.9085i	0.439566	−	0.551199i
$834$	−0.645260	+	0.310741i	−0.0223435	+	0.0107601i
$835$	0.606564	+	2.65753i	0.0209910	+	0.0919676i
$836$	0.385002	−	1.68681i	0.0133156	−	0.0583394i
$837$	26.5954	+	12.8077i	0.919273	+	0.442699i
$838$	−19.7877	+	9.52925i	−0.683555	+	0.329183i
$839$	5.93578	−	26.0064i	0.204926	−	0.897839i	−0.762959	−	0.646446i	$-0.776254\pi$
$839$	5.93578	−	26.0064i	0.204926	−	0.897839i	0.967885	−	0.251393i	$-0.0808885\pi$
$840$	0.0120816			0.000416854
$841$	−25.1084	+	14.5111i	−0.865805	+	0.500381i
$842$	−40.4349			−1.39348
$843$	2.56398	−	11.2335i	0.0883083	−	0.386904i
$844$	15.1359	−	7.28905i	0.520998	−	0.250899i
$845$	−0.448927	−	0.216192i	−0.0154435	−	0.00743722i
$846$	−0.480386	+	2.10471i	−0.0165160	+	0.0723613i
$847$	0.225446	+	0.987745i	0.00774643	+	0.0339393i
$848$	−7.50969	+	3.61648i	−0.257884	+	0.124190i
$849$	6.00232	−	7.52667i	0.205999	−	0.258315i
$850$	−9.00634	+	11.2936i	−0.308915	+	0.387367i
$851$	21.2458	+	10.2314i	0.728296	+	0.350729i
$852$	−3.78836	−	4.75046i	−0.129787	−	0.162748i
$853$	−19.7071			−0.674758			−0.337379	−	0.941369i	$-0.609540\pi$
$853$	−19.7071			−0.674758			−0.337379	+	0.941369i	$0.609540\pi$
$854$	0.757865	+	0.950332i	0.0259336	+	0.0325197i
$855$	0.153752	+	0.673633i	0.00525822	+	0.0230378i
$856$	−3.66972	−	16.0781i	−0.125428	−	0.549538i
$857$	1.34481	+	1.68634i	0.0459380	+	0.0576044i	0.804270	−	0.594264i	$-0.202557\pi$
$857$	1.34481	+	1.68634i	0.0459380	+	0.0576044i	−0.758332	+	0.651869i	$0.773985\pi$
$858$	−2.91856			−0.0996380
$859$	21.4799	+	26.9349i	0.732883	+	0.919006i	0.998990	−	0.0449372i	$-0.0143088\pi$
$859$	21.4799	+	26.9349i	0.732883	+	0.919006i	−0.266107	+	0.963944i	$0.585737\pi$
$860$	1.18933	+	0.572753i	0.0405559	+	0.0195307i
$861$	−0.143104	+	0.179447i	−0.00487698	+	0.00611553i
$862$	13.7796	−	17.2791i	0.469336	−	0.588529i
$863$	8.63922	−	4.16043i	0.294082	−	0.141623i	−0.281025	−	0.959700i	$-0.590674\pi$
$863$	8.63922	−	4.16043i	0.294082	−	0.141623i	0.575108	+	0.818078i	$0.304960\pi$
$864$	0.702907	+	3.07964i	0.0239134	+	0.104771i
$865$	0.00527135	−	0.0230953i	0.000179231	−	0.000785263i
$866$	−3.50216	−	1.68655i	−0.119008	−	0.0573113i
$867$	−4.26055	+	2.05177i	−0.144696	+	0.0696819i
$868$	0.228562	−	1.00139i	0.00775789	−	0.0339895i
$869$	−6.52888			−0.221477
$870$	−0.153325	−	0.571714i	−0.00519821	−	0.0193829i
$871$	−43.3290			−1.46815
$872$	0.632219	−	2.76993i	0.0214096	−	0.0938017i
$873$	−25.6896	+	12.3715i	−0.869462	+	0.418711i
$874$	9.09515	+	4.37999i	0.307648	+	0.148155i
$875$	0.0482534	−	0.211412i	0.00163126	−	0.00714702i
$876$	0.981582	+	4.30059i	0.0331646	+	0.145304i
$877$	0.758824	−	0.365430i	0.0256237	−	0.0123397i	−0.421028	−	0.907048i	$-0.638331\pi$
$877$	0.758824	−	0.365430i	0.0256237	−	0.0123397i	0.446652	+	0.894708i	$0.352616\pi$
$878$	−6.33310	+	7.94146i	−0.213732	+	0.268011i
$879$	−6.06481	+	7.60503i	−0.204561	+	0.256511i
$880$	0.238250	+	0.114735i	0.00803142	+	0.00386773i
$881$	−5.13019	−	6.43306i	−0.172841	−	0.216735i	0.687864	−	0.725839i	$-0.258548\pi$
$881$	−5.13019	−	6.43306i	−0.172841	−	0.216735i	−0.860705	+	0.509104i	$0.829977\pi$
$882$	−18.8116			−0.633420
$883$	33.8568	+	42.4551i	1.13937	+	1.42873i	0.887404	+	0.460993i	$0.152507\pi$
$883$	33.8568	+	42.4551i	1.13937	+	1.42873i	0.251969	+	0.967735i	$0.418922\pi$
$884$	2.55227	+	11.1822i	0.0858421	+	0.376099i
$885$	−0.124449	−	0.545248i	−0.00418332	−	0.0183283i
$886$	−12.0312	−	15.0866i	−0.404195	−	0.506844i
$887$	−13.5013			−0.453328			−0.226664	−	0.973973i	$-0.572782\pi$
$887$	−13.5013			−0.453328			−0.226664	+	0.973973i	$0.572782\pi$
$888$	−1.04743	−	1.31343i	−0.0351493	−	0.0440758i
$889$	0.268217	+	0.129167i	0.00899572	+	0.00433211i
$890$	1.41939	−	1.77985i	0.0475780	−	0.0596609i
$891$	−5.26354	+	6.60027i	−0.176335	+	0.221117i
$892$	1.29105	−	0.621738i	0.0432276	−	0.0208173i
$893$	−0.231250	−	1.01317i	−0.00773849	−	0.0339045i
$894$	0.827060	−	3.62359i	0.0276610	−	0.121191i
$895$	2.26271	+	1.08966i	0.0756340	+	0.0364234i
$896$	0.0990311	−	0.0476909i	0.00330840	−	0.00159324i
$897$	3.78919	−	16.6015i	0.126517	−	0.554309i
$898$	−21.6394			−0.722116
$899$	−50.2878	+	1.89272i	−1.67719	+	0.0631257i
$900$	13.3545			0.445150
$901$	5.40073	−	23.6622i	0.179924	−	0.788301i
$902$	−4.52619	+	2.17970i	−0.150706	+	0.0725760i
$903$	−0.366289	−	0.176396i	−0.0121893	−	0.00587007i
$904$	3.48792	−	15.2816i	0.116006	−	0.508257i
$905$	−0.314446	−	1.37768i	−0.0104525	−	0.0457956i
$906$	4.74698	−	2.28602i	0.157708	−	0.0759481i
$907$	−28.9795	+	36.3391i	−0.962248	+	1.20662i	0.0161456	+	0.999870i	$0.494860\pi$
$907$	−28.9795	+	36.3391i	−0.962248	+	1.20662i	−0.978394	+	0.206751i	$0.933711\pi$
$908$	−8.36443	+	10.4887i	−0.277583	+	0.348078i
$909$	14.4867	+	6.97644i	0.480494	+	0.231394i
$910$	−0.0534662	−	0.0670445i	−0.00177239	−	0.00222250i
$911$	21.1685			0.701344			0.350672	−	0.936498i	$-0.385953\pi$
$911$	21.1685			0.701344			0.350672	+	0.936498i	$0.385953\pi$
$912$	−0.448394	−	0.562269i	−0.0148478	−	0.0186186i
$913$	−3.46844	−	15.1962i	−0.114788	−	0.502921i
$914$	0.563155	+	2.46734i	0.0186275	+	0.0816124i
$915$	0.757865	+	0.950332i	0.0250542	+	0.0314170i
$916$	11.5090			0.380269
$917$	−1.00149	−	1.25583i	−0.0330722	−	0.0414712i
$918$	−8.28717	−	3.99089i	−0.273517	−	0.131719i
$919$	−12.5699	+	15.7621i	−0.414641	+	0.519944i	−0.944664	−	0.328040i	$-0.893612\pi$
$919$	−12.5699	+	15.7621i	−0.414641	+	0.519944i	0.530023	+	0.847984i	$0.322183\pi$
$920$	−0.961968	+	1.20627i	−0.0317151	+	0.0397695i
$921$	15.1809	−	7.31074i	0.500228	−	0.240897i
$922$	2.39493	+	10.4929i	0.0788728	+	0.345564i
$923$	−9.59664	+	42.0456i	−0.315877	+	1.38395i
$924$	−0.0733760	−	0.0353360i	−0.00241389	−	0.00116247i
$925$	−13.5298	+	6.51563i	−0.444858	+	0.214232i
$926$	−1.36270	+	5.97038i	−0.0447811	+	0.196199i
$927$	38.7482			1.27266
$928$	−3.51357	−	4.08103i	−0.115339	−	0.133966i
$929$	19.7952			0.649461			0.324730	−	0.945807i	$-0.394726\pi$
$929$	19.7952			0.649461			0.324730	+	0.945807i	$0.394726\pi$
$930$	0.228562	−	1.00139i	0.00749483	−	0.0328370i
$931$	8.15883	−	3.92909i	0.267395	−	0.128771i
$932$	0.662718	+	0.319148i	0.0217081	+	0.0104541i
$933$	−2.93751	+	12.8701i	−0.0961697	+	0.421347i
$934$	7.78017	+	34.0871i	0.254575	+	1.11537i
$935$	−0.693750	+	0.334093i	−0.0226881	+	0.0109260i
$936$	6.61141	−	8.29044i	0.216101	−	0.270982i
$937$	−34.9705	+	43.8516i	−1.14244	+	1.43257i	−0.257853	+	0.966184i	$0.583015\pi$
$937$	−34.9705	+	43.8516i	−1.14244	+	1.43257i	−0.884582	+	0.466384i	$0.845556\pi$
$938$	−1.08934	−	0.524600i	−0.0355683	−	0.0171288i
$939$	9.92171	+	12.4414i	0.323783	+	0.406011i
$940$	0.158834			0.00518058
$941$	−1.50066	−	1.88177i	−0.0489202	−	0.0613441i	0.756769	−	0.653682i	$-0.226777\pi$
$941$	−1.50066	−	1.88177i	−0.0489202	−	0.0613441i	−0.805690	+	0.592338i	$0.798205\pi$
$942$	−1.16003	−	5.08242i	−0.0377958	−	0.165594i
$943$	−6.52230	−	28.5761i	−0.212395	−	0.930565i
$944$	−3.17241	−	3.97807i	−0.103253	−	0.129475i
$945$	0.0687686			0.00223704
$946$	−5.54809	−	6.95708i	−0.180384	−	0.226194i
$947$	−2.16003	−	1.04022i	−0.0701915	−	0.0338025i	0.398459	−	0.917186i	$-0.369545\pi$
$947$	−2.16003	−	1.04022i	−0.0701915	−	0.0338025i	−0.468650	+	0.883384i	$0.655260\pi$
$948$	−1.69202	+	2.12173i	−0.0549543	+	0.0689105i
$949$	19.5214	−	24.4791i	0.633692	−	0.794624i
$950$	−5.79201	+	2.78929i	−0.187918	+	0.0904964i
$951$	−0.933329	−	4.08918i	−0.0302653	−	0.132601i
$952$	−0.0712201	+	0.312036i	−0.00230826	+	0.0101131i
$953$	30.1634	+	14.5259i	0.977090	+	0.470542i	0.853103	−	0.521742i	$-0.174718\pi$
$953$	30.1634	+	14.5259i	0.977090	+	0.470542i	0.123987	+	0.992284i	$0.460432\pi$
$954$	−20.2162	+	9.73563i	−0.654525	+	0.315203i
$955$	−0.140948	+	0.617534i	−0.00456098	+	0.0199829i
$956$	0.0881460			0.00285085
$957$	−0.740939	+	3.92068i	−0.0239512	+	0.126738i
$958$	30.8732			0.997468
$959$	0.0389917	−	0.170834i	0.00125911	−	0.00551651i
$960$	0.0990311	−	0.0476909i	0.00319622	−	0.00153922i
$961$	−50.7476	−	24.4387i	−1.63702	−	0.788347i
$962$	−2.65333	+	11.6250i	−0.0855466	+	0.374804i
$963$	−9.87896	−	43.2826i	−0.318345	−	1.39476i
$964$	5.59783	−	2.69578i	0.180294	−	0.0868251i
$965$	−1.86108	+	2.33372i	−0.0599102	+	0.0751250i
$966$	0.296265	−	0.371505i	0.00953218	−	0.0119530i
$967$	−31.6906	−	15.2614i	−1.01910	−	0.490773i	−0.151723	−	0.988423i	$-0.548482\pi$
$967$	−31.6906	−	15.2614i	−1.01910	−	0.490773i	−0.867378	+	0.497650i	$0.834196\pi$
$968$	5.74698	+	7.20648i	0.184715	+	0.231625i
$969$	2.09411			0.0672726
$970$	1.30798	+	1.64015i	0.0419967	+	0.0526621i
$971$	6.12671	+	26.8429i	0.196616	+	0.861429i	0.972933	+	0.231087i	$0.0742282\pi$
$971$	6.12671	+	26.8429i	0.196616	+	0.861429i	−0.776318	+	0.630342i	$0.782915\pi$
$972$	2.88955	+	12.6600i	0.0926824	+	0.406068i
$973$	0.0884415	+	0.110902i	0.00283530	+	0.00355536i
$974$	0.408206			0.0130798
$975$	6.76122	+	8.47830i	0.216532	+	0.271523i
$976$	9.96346	+	4.79815i	0.318923	+	0.153585i
$977$	−7.08240	+	8.88105i	−0.226586	+	0.284130i	−0.882109	−	0.471045i	$-0.843877\pi$
$977$	−7.08240	+	8.88105i	−0.226586	+	0.284130i	0.655523	+	0.755175i	$0.272448\pi$
$978$	−5.62916	+	7.05875i	−0.180001	+	0.225714i
$979$	−13.8262	+	6.65833i	−0.441886	+	0.212801i
$980$	0.307979	+	1.34934i	0.00983801	+	0.0431032i
$981$	1.70195	−	7.45672i	0.0543390	−	0.238075i
$982$	18.1652	+	8.74788i	0.579674	+	0.279156i
$983$	29.6589	−	14.2830i	0.945972	−	0.455556i	0.103700	−	0.994609i	$-0.466932\pi$
$983$	29.6589	−	14.2830i	0.945972	−	0.455556i	0.842272	+	0.539053i	$0.181218\pi$
$984$	−0.464656	+	2.03579i	−0.0148127	+	0.0648987i
$985$	−2.87561			−0.0916245
$986$	15.6697	−	0.589773i	0.499026	−	0.0187822i
$987$	−0.0489173			−0.00155706
$988$	−1.13587	+	4.97656i	−0.0361367	+	0.158325i
$989$	46.7769	−	22.5266i	1.48742	−	0.716303i
$990$	0.641375	+	0.308870i	0.0203842	+	0.00981653i
$991$	−5.00258	+	21.9177i	−0.158912	+	0.696240i	0.831201	+	0.555972i	$0.187654\pi$
$991$	−5.00258	+	21.9177i	−0.158912	+	0.696240i	−0.990114	+	0.140269i	$0.955203\pi$
$992$	−2.07942	−	9.11052i	−0.0660215	−	0.289259i
$993$	−5.59299	+	2.69344i	−0.177488	+	0.0854738i
$994$	−0.750332	+	0.940887i	−0.0237991	+	0.0298431i
$995$	3.27599	−	4.10796i	0.103856	−	0.130231i
$996$	−5.83728	−	2.81109i	−0.184961	−	0.0890727i
$997$	−13.7943	−	17.2975i	−0.436871	−	0.547819i	0.513845	−	0.857883i	$-0.328221\pi$
$997$	−13.7943	−	17.2975i	−0.436871	−	0.547819i	−0.950716	+	0.310065i	$0.899649\pi$
$998$	10.3787			0.328531
$999$	−5.96197	−	7.47607i	−0.188628	−	0.236532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.2.d.a.25.1	yes	6
3.2	odd	2		522.2.k.c.199.1		6
4.3	odd	2		464.2.u.b.257.1		6
29.6	even	14		1682.2.a.n.1.2		3
29.7	even	7	inner	58.2.d.a.7.1	✓	6
29.14	odd	28		1682.2.b.g.1681.5		6
29.15	odd	28		1682.2.b.g.1681.2		6
29.23	even	7		1682.2.a.m.1.2		3
87.65	odd	14		522.2.k.c.181.1		6
116.7	odd	14		464.2.u.b.65.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.a.7.1	✓	6	29.7	even	7	inner
58.2.d.a.25.1	yes	6	1.1	even	1	trivial
464.2.u.b.65.1		6	116.7	odd	14
464.2.u.b.257.1		6	4.3	odd	2
522.2.k.c.181.1		6	87.65	odd	14
522.2.k.c.199.1		6	3.2	odd	2
1682.2.a.m.1.2		3	29.23	even	7
1682.2.a.n.1.2		3	29.6	even	14
1682.2.b.g.1681.2		6	29.15	odd	28
1682.2.b.g.1681.5		6	29.14	odd	28

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(0.500000 - 0.240787i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.0440730 + 0.193096i) q^{5} +(-0.123490 - 0.541044i) q^{6} +(-0.0990311 + 0.0476909i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(-1.67845 + 2.10471i) q^{9} +(0.178448 + 0.0859360i) q^{10} +(-0.832437 - 1.04384i) q^{11} -0.554958 q^{12} +(2.45593 + 3.07964i) q^{13} +(0.0244587 + 0.107160i) q^{14} +(0.0244587 + 0.107160i) q^{15} +(0.623490 + 0.781831i) q^{16} -2.91185 q^{17} +(1.67845 + 2.10471i) q^{18} +(-1.16756 - 0.562269i) q^{19} +(0.123490 - 0.154851i) q^{20} +(-0.0380322 + 0.0476909i) q^{21} +(-1.20291 + 0.579289i) q^{22} +(-1.73341 - 7.59455i) q^{23} +(-0.123490 + 0.541044i) q^{24} +(4.46950 + 2.15240i) q^{25} +(3.54892 - 1.70907i) q^{26} +(-0.702907 + 3.07964i) q^{27} +0.109916 q^{28} +(-1.39493 - 5.20136i) q^{29} +0.109916 q^{30} +(2.07942 - 9.11052i) q^{31} +(0.900969 - 0.433884i) q^{32} +(-0.667563 - 0.321481i) q^{33} +(-0.647948 + 2.83885i) q^{34} +(-0.00484434 - 0.0212244i) q^{35} +(2.42543 - 1.16802i) q^{36} +(-1.88740 + 2.36672i) q^{37} +(-0.807979 + 1.01317i) q^{38} +(1.96950 + 0.948461i) q^{39} +(-0.123490 - 0.154851i) q^{40} +3.76271 q^{41} +(0.0380322 + 0.0476909i) q^{42} +(1.48307 + 6.49777i) q^{43} +(0.297093 + 1.30165i) q^{44} +(-0.332437 - 0.416863i) q^{45} -7.78986 q^{46} +(0.500000 + 0.626980i) q^{47} +(0.500000 + 0.240787i) q^{48} +(-4.35690 + 5.46337i) q^{49} +(3.09299 - 3.87849i) q^{50} +(-1.45593 + 0.701137i) q^{51} +(-0.876510 - 3.84024i) q^{52} +(-1.85474 + 8.12615i) q^{53} +(2.84601 + 1.37057i) q^{54} +(0.238250 - 0.114735i) q^{55} +(0.0244587 - 0.107160i) q^{56} -0.719169 q^{57} +(-5.38135 + 0.202542i) q^{58} -5.08815 q^{59} +(0.0244587 - 0.107160i) q^{60} +(9.96346 - 4.79815i) q^{61} +(-8.41939 - 4.05456i) q^{62} +(0.0658433 - 0.288478i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.702907 + 0.338502i) q^{65} +(-0.461968 + 0.579289i) q^{66} +(-6.85839 + 8.60015i) q^{67} +(2.62349 + 1.26341i) q^{68} +(-2.69537 - 3.37989i) q^{69} -0.0217703 q^{70} +(6.82640 + 8.56003i) q^{71} +(-0.599031 - 2.62453i) q^{72} +(-1.76875 - 7.74940i) q^{73} +(1.88740 + 2.36672i) q^{74} +2.75302 q^{75} +(0.807979 + 1.01317i) q^{76} +(0.132219 + 0.0636733i) q^{77} +(1.36294 - 1.70907i) q^{78} +(3.04892 - 3.82322i) q^{79} +(-0.178448 + 0.0859360i) q^{80} +(-1.40701 - 6.16451i) q^{81} +(0.837282 - 3.66837i) q^{82} +(10.5184 + 5.06540i) q^{83} +(0.0549581 - 0.0264664i) q^{84} +(0.128334 - 0.562269i) q^{85} +6.66487 q^{86} +(-1.94989 - 2.26480i) q^{87} +1.33513 q^{88} +(2.55765 - 11.2058i) q^{89} +(-0.480386 + 0.231342i) q^{90} +(-0.390084 - 0.187854i) q^{91} +(-1.73341 + 7.59455i) q^{92} +(-1.15399 - 5.05596i) q^{93} +(0.722521 - 0.347948i) q^{94} +(0.160030 - 0.200671i) q^{95} +(0.346011 - 0.433884i) q^{96} +(9.54288 + 4.59561i) q^{97} +(4.35690 + 5.46337i) q^{98} +3.59419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 3 q^{3} - q^{4} - 4 q^{5} + 4 q^{6} - 5 q^{7} + q^{8} - 6 q^{9} - 3 q^{10} - 6 q^{11} - 4 q^{12} + 11 q^{13} - 9 q^{14} - 9 q^{15} - q^{16} - 10 q^{17} + 6 q^{18} - 6 q^{19} - 4 q^{20}+ \cdots + 48 q^{99}+O(q^{100}) \) 6 * q + q^2 + 3 * q^3 - q^4 - 4 * q^5 + 4 * q^6 - 5 * q^7 + q^8 - 6 * q^9 - 3 * q^10 - 6 * q^11 - 4 * q^12 + 11 * q^13 - 9 * q^14 - 9 * q^15 - q^16 - 10 * q^17 + 6 * q^18 - 6 * q^19 - 4 * q^20 + 15 * q^21 + 6 * q^22 - 7 * q^23 + 4 * q^24 + 17 * q^25 + 3 * q^26 + 9 * q^27 + 2 * q^28 + 15 * q^29 + 2 * q^30 + 4 * q^31 + q^32 - 3 * q^33 + 10 * q^34 + 22 * q^35 + q^36 - 13 * q^37 - 15 * q^38 + 2 * q^39 + 4 * q^40 - 12 * q^41 - 15 * q^42 - 7 * q^43 + 15 * q^44 - 3 * q^45 + 3 * q^47 + 3 * q^48 - 18 * q^49 + 4 * q^50 - 5 * q^51 - 10 * q^52 - 22 * q^53 + 12 * q^54 - 24 * q^55 - 9 * q^56 + 18 * q^57 - 15 * q^58 - 38 * q^59 - 9 * q^60 + 31 * q^61 - 18 * q^62 - 2 * q^63 - q^64 + 9 * q^65 - 18 * q^66 + 11 * q^67 + 11 * q^68 - 28 * q^69 + 6 * q^70 + 23 * q^71 - 8 * q^72 + 5 * q^73 + 13 * q^74 + 26 * q^75 + 15 * q^76 + 12 * q^77 + 19 * q^78 + 3 * q^80 - 23 * q^81 - 16 * q^82 + 35 * q^83 + q^84 - 26 * q^85 + 42 * q^86 + 11 * q^87 + 6 * q^88 + 13 * q^89 + 10 * q^90 - q^91 - 7 * q^92 - 12 * q^93 + 4 * q^94 + 25 * q^95 - 3 * q^96 + 20 * q^97 + 18 * q^98 + 48 * q^99

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